Math Solver with Steps: Get & Check Step-by-Step Answers

A math solver with steps takes your problem (typed, or as a photo) and returns the full worked solution: every transformation, the rule behind it, and a final answer you can check. To get steps you can trust, do three things: enter the problem without ambiguity, ask for each step to be named, and verify the answer by substituting it back. You can try this right now in the free MathAI GPT math solver, or on your phone with the iPhone app or Android app.

This guide shows what “with steps” should actually mean, how to type problems so the solver reads them correctly, six fully worked examples (each with a check), and the mistakes a good set of steps helps you catch.

1) What a good step-by-step solution looks like

Not every “solution with steps” is equally useful. A final answer with two lines of working skips exactly the part you need. Before you rely on any solver (or any worked example in a textbook), look for these six things:

It restates the problem. You can confirm the solver solved your problem, not a misread version.
One change per line. Each line does a single thing: distribute, combine like terms, subtract from both sides.
Each step names its rule. “Distributive property,” “chain rule,” “multiply both sides by 12.”
Equations stay balanced. Whatever happens on one side happens on the other.
The final answer is clearly marked, with units for word problems.
It ends with a check: substitution, a second method, or a quick estimate.

If a solution is missing the check, ask for one. In MathAI GPT a prompt like “Solve step by step, name the rule for each step, then verify the answer” produces exactly this format.

2) How to enter a problem so the steps come out right

Most “wrong” answers from a solver are really ambiguous input. The solver can only follow the problem it reads. These are the most common traps:

You type	It can mean	Type this instead
1/2x	(1/2)·x or 1/(2x)	(1/2)x or 1/(2x)
x+1/x-1	x + (1/x) − 1	(x+1)/(x-1)
-3^2	−9 (standard order) or 9	(-3)^2 if you mean 9
2^x+1	2^x + 1 or 2^x+1	2^(x+1)
sin x^2	sin(x²) or (sin x)²	sin(x^2) or (sin(x))^2

A few more habits that save time:

Say what you want. “Solve for x,” “simplify,” “factor,” and “find the derivative” are different tasks.
Include the whole word problem, including units and any constraint such as “x is a positive integer.”
For photos, crop to one problem, keep the page flat and well lit, and check the solver's restated problem before reading the steps. Our photo math solver guide covers this in detail.

3) Six worked examples (with checks)

Here is what complete steps look like across the topics students ask about most. Try each one yourself first, then compare.

Example 1: A linear equation

Solve 3(x − 4) + 5 = 2x + 7.

3x − 12 + 5 = 2x + 7 — distributive property
3x − 7 = 2x + 7 — combine like terms (−12 + 5 = −7)
x − 7 = 7 — subtract 2x from both sides
x = 14 — add 7 to both sides

Check

Left side: 3(14 − 4) + 5 = 3(10) + 5 = 35. Right side: 2(14) + 7 = 35. Both sides equal 35, so x = 14 is correct.

More practice: how to solve linear equations.

Example 2: An equation with fractions

Solve x/3 + (x − 1)/4 = 5.

12 · (x/3) + 12 · ((x − 1)/4) = 12 · 5 — multiply every term by the LCD, 12
4x + 3(x − 1) = 60 — simplify each term
4x + 3x − 3 = 60 — distributive property
7x − 3 = 60 — combine like terms
7x = 63 — add 3 to both sides
x = 9 — divide both sides by 7

Check

9/3 + (9 − 1)/4 = 3 + 8/4 = 3 + 2 = 5. Correct.

The key move is clearing denominators in one step. A good solver names the LCD instead of jumping straight to line 2.

Example 3: A system of two equations

Solve the system 2x + 3y = 12 and x − y = 1.

x = y + 1 — solve the second equation for x
2(y + 1) + 3y = 12 — substitute into the first equation
2y + 2 + 3y = 12 — distributive property
5y + 2 = 12 — combine like terms
5y = 10, so y = 2 — subtract 2, then divide by 5
x = 2 + 1 = 3 — back-substitute into x = y + 1

Check

First equation: 2(3) + 3(2) = 6 + 6 = 12. Second equation: 3 − 2 = 1. The solution (3, 2) satisfies both.

A system is only solved when the answer works in every equation. See how to solve systems of equations for elimination and graphing methods.

Example 4: A quadratic equation (two methods)

Solve 2x² − 3x − 5 = 0.

Method A: factoring

a·c = 2 · (−5) = −10 — find two numbers that multiply to −10 and add to −3: −5 and 2
2x² − 5x + 2x − 5 = 0 — split the middle term
x(2x − 5) + 1(2x − 5) = 0 — factor by grouping
(2x − 5)(x + 1) = 0 — factor out (2x − 5)
x = 5/2 or x = −1 — zero product property

Method B: quadratic formula

a = 2, b = −3, c = −5 — identify coefficients
b² − 4ac = 9 − 4(2)(−5) = 9 + 40 = 49 — discriminant; positive, so two real roots
x = (3 ± √49) / 4 = (3 ± 7) / 4 — x = (−b ± √(b² − 4ac)) / 2a
x = 10/4 = 5/2 or x = −4/4 = −1 — evaluate both signs

Check

Both methods give x = 5/2 and x = −1. Substituting x = 5/2: 2(25/4) − 3(5/2) − 5 = 12.5 − 7.5 − 5 = 0. Substituting x = −1: 2 + 3 − 5 = 0.

Asking for a second method is one of the best ways to check a solver. Practice more with solving quadratic equations step by step.

Example 5: A derivative with the chain rule

Find the derivative of f(x) = (3x² + 1)⁴.

outer function u⁴, inner function u = 3x² + 1 — identify the composition
d/dx[u⁴] = 4u³ · du/dx — chain rule
du/dx = 6x — power rule on the inner function
f′(x) = 4(3x² + 1)³ · 6x = 24x(3x² + 1)³ — multiply and simplify

Check

At x = 1 the formula gives 24 · 1 · (4)³ = 24 · 64 = 1536. A numerical estimate, [f(1.00001) − f(0.99999)] / 0.00002, also comes out to about 1536, so the derivative is right.

The classic mistake here is forgetting the inner derivative (6x). For power, product, quotient and chain rule practice, see the derivative guide.

Example 6: A percent word problem

A jacket costs $80 after a 20% discount. What was the original price?

Let p = original price — define the variable
p − 0.20p = 0.80p — a 20% discount leaves 80% of the price
0.80p = 80 — write the equation
p = 80 / 0.80 = 100 — divide both sides by 0.80

Check

20% of $100 is $20, and $100 − $20 = $80. The original price was $100.

The common wrong answer is $80 × 1.20 = $96, which adds 20% of the sale price instead of undoing a discount on the original price. Writing the equation first, as above, prevents it.

4) How to check any solution in under a minute

Steps are only valuable if you can verify them. These checks work for almost everything:

Substitute back. Plug the answer into the original equation, not a later line that might already contain an error.
Reverse the operation. Multiply out a factorization, differentiate an antiderivative, or multiply a quotient by the divisor.
Use a second method. Factoring vs. the quadratic formula, substitution vs. elimination.
Estimate. If 0.80p = 80, p must be a bit more than 80. An answer of 64 is obviously wrong.
Check units and sense. A negative length, or a probability above 1, means something went wrong.

5) Mistakes that good steps help you catch

Seeing every line is what lets you spot the errors that a bare answer hides. Three classics:

Dividing by a variable (and losing a solution)

Solving x² = 5x by dividing both sides by x gives only x = 5. The correct steps move everything to one side: x² − 5x = 0, so x(x − 5) = 0, so x = 0 or x = 5. Dividing by x silently threw away x = 0.

Extraneous roots after squaring

Solve √(x + 3) = x − 3:

x + 3 = (x − 3)² = x² − 6x + 9 — square both sides
0 = x² − 7x + 6 — move all terms to one side
0 = (x − 1)(x − 6) — factor
x = 1 or x = 6 — zero product property

Check

x = 6: √9 = 3 and 6 − 3 = 3, which works. x = 1: √4 = 2 but 1 − 3 = −2, which fails. Squaring created the extra root, so the only solution is x = 6. Skipping the check here gives a wrong answer.

Sign errors when distributing a negative

5 − 2(x − 3) equals 5 − 2x + 6 = 11 − 2x, not 5 − 2x − 6. The −2 multiplies both terms inside the parentheses. When your answer and the solver's differ, the line where you distributed a negative is the first place to look.

6) Use the steps to learn, not just to finish

A step-by-step solver is most useful as a tutor. Students who just copy the final line are back to square one on the test. This routine works better:

Try first. Get as far as you can on paper.
Ask for a hint, not the solution. “Give me only the first step and wait for my attempt.”
Compare line by line. Find the exact line where your work and the solution split.
Ask why. “Why is this step allowed?” turns a fix into understanding.
Do a similar problem alone. Ask for a new problem with different numbers and solve it without help.

Copy/paste prompts

“Solve step by step. Name the rule for each step. Then verify by substitution.”
“Show a second method and confirm both give the same answer.”
“Here is my work: [paste]. Find the first line with a mistake and explain it.”
“Give me two similar practice problems, then check my answers.”

Not sure whether you need a solver or a tutoring-style chat? Read math solver vs. math GPT.

7) Get step-by-step solutions on the web or on your phone

MathAI GPT is built around exactly this workflow: you type a problem or upload a picture, and it returns a worked, step-by-step solution you can question, re-check, or ask to explain differently.

On the web: open the free math solver with steps. Nothing to install, and there is a free daily allowance.
On iPhone: get MathAI GPT - Math Solver on the App Store. Snap a photo of a handwritten or printed problem and get the steps.
On Android: get MathAI GPT on Google Play.

Whichever you use, the rules from this guide still apply: enter the problem clearly, read every step, and check the answer.

Frequently asked questions

Is there a free math solver with steps?

Yes. The MathAI GPT web solver at mathaigpt.com has a free tier with a daily limit, and it shows step-by-step solutions for typed problems and photos. The iPhone and Android apps are free to download.

Can a math solver show steps from a photo of my homework?

Yes. Upload a clear photo or screenshot and the solver reads the problem, then solves it step by step. Always compare the problem it read with your original before trusting the steps, because a misread sign or exponent changes the whole solution.

Are AI math solvers always right?

No tool is right 100% of the time. That is why steps matter: you can check each line, substitute the answer back into the original problem, and ask for a second method. If two methods agree and the check works, you can be confident in the answer.

Is using a step-by-step math solver cheating?

It depends on how you use it and on your teacher’s rules. Copying the final answer teaches nothing. Using the steps to find where you went wrong, asking for a hint first, and then solving a similar problem on your own is a legitimate way to learn.

What kinds of math can a solver with steps handle?

Arithmetic, fractions and percentages, linear and quadratic equations, systems of equations, inequalities, exponents and logarithms, trigonometry, statistics, derivatives and integrals, and word problems. Clear input matters more than the topic.

What is the difference between a calculator and a math solver with steps?

A calculator returns a number. A math solver with steps shows the method: each transformation, the rule that justifies it, and a final check. Use a calculator for quick arithmetic and a step-by-step solver when you need to understand or show your work.

Try it now

Pick one problem from your homework, type it into the MathAI GPT solver with the prompt “Solve step by step, name each rule, then verify,” and check the result using one of the methods above.