Free Equation Solver
Paste any equation — linear, quadratic, polynomial, rational, exponential or logarithmic — and get every step of the solution. Built for Class 6 to 12 and entrance-exam prep. Free plan to start.
💡 You can also paste an image with Ctrl+V or drag a file here.
Learn
A worked linear equation — isolating the variable step by step
Below is one fully worked example plus a short primer so you can see exactly how our AI reasons through a problem.
Example Problem
DEMO3(x - 2) + 4 = 2x + 5
- 1
Expand the bracket on the left
Distribute the 3 across (x − 2), then combine the constants on the same side.
- 2
Simplify the left side
−6 + 4 = −2, so the left side becomes 3x − 2.
- 3
Collect x terms on one side
Subtract 2x from both sides and add 2 to both sides so x is isolated.
- 4
Solve for x
- 5
Verify
Plug x = 7: left = 3(7 − 2) + 4 = 15 + 4 = 19. Right = 2(7) + 5 = 19. ✓
Final Answer
How to solve any equation — a strategy by degree
An equation is a statement that two expressions are equal, written with an = sign between them. Solving it means finding every value of the variable that makes the statement true. The golden rule never changes no matter how complicated the equation looks: whatever you do to one side, do to the other — add, subtract, multiply, divide, square, take a log — and the equation stays balanced.
School maths groups equations into families by the highest power of the variable. Linear equations have degree 1 (3x + 4 = 10) and always have exactly one solution. Quadratic equations have degree 2 (x² − 5x + 6 = 0) and can have zero, one or two real solutions depending on the discriminant b² − 4ac. Cubic and higher-degree polynomial equations can have up to as many solutions as their degree. Rational equations have the variable in a denominator, exponential equations have it in an exponent (2^x = 32), and logarithmic equations have it inside a log.
The solving strategy depends on the family. Linear — isolate x. Quadratic — factor, complete the square, or use the quadratic formula. Polynomial — try rational-root theorem, then factor. Rational — multiply through by the denominator, then solve the resulting polynomial, then check for extraneous roots (values that make the original denominator zero). Exponential and logarithmic — take logs or exponentiate both sides to get back to a polynomial.
The solver above handles all of these. Paste the equation exactly as written in your textbook or photograph the page. The AI identifies which family the equation belongs to, picks the right method, and shows every step — including the verification, which is where most exam marks are lost.
Equations to practise (linear, quadratic, polynomial)
Tap any problem to solve it with full step-by-step working.
- Solve with AI →
1. 5x - 7 = 3x + 9
LinearClass 7–8Easy - Solve with AI →
2. x^2 - 8x + 15 = 0
QuadraticClass 10Medium - Solve with AI →
3. 2x^3 - 5x^2 - x + 6 = 0
CubicClass 11Hard - Solve with AI →
4. (x + 1)/(x - 3) = 2
RationalClass 9–10Medium - Solve with AI →
5. 2^{x + 1} = 32
ExponentialClass 11Medium
Frequently asked questions
What types of equations can the solver handle?+
Linear, quadratic, cubic and higher-degree polynomials, simultaneous equations in two or more variables, rational equations with variables in the denominator, exponential and logarithmic equations, and trigonometric equations. If you can write it with an equals sign, paste it in.
How do I solve an equation step by step?+
Identify the highest power of the variable (the degree), which tells you the family. Then: move all variable terms to one side and constants to the other, simplify, and apply the solving method for that family — isolation for linear, the quadratic formula for degree-2, factoring or the rational-root theorem for higher polynomials. Always verify by substituting the answer back into the original equation.
What is the difference between an equation and an expression?+
An expression is a combination of numbers, variables and operators with no equals sign (e.g. 3x + 4). An equation sets two expressions equal to each other (e.g. 3x + 4 = 10). You simplify expressions; you solve equations.
Why does my quadratic equation have no real solutions?+
When the discriminant b² − 4ac is negative, the quadratic has no real roots — only complex ones. Geometrically this means the parabola y = ax² + bx + c never crosses the x-axis. The solver flags this explicitly and shows the complex roots when asked (Class 11 and above in CBSE).
What are extraneous solutions and why do rational equations have them?+
When you multiply both sides of a rational equation by the denominator, you may introduce solutions that make the original denominator zero — these are extraneous because the original equation is undefined there. Always substitute each candidate solution back into the original equation and discard any that make a denominator zero.
Can the solver handle equations from a photo of my homework?+
Yes. Tap the Image or PDF button or drag a photo of the page into the box. The AI reads printed or handwritten equations, identifies the family, solves and shows working — same output as if you typed it in.
Does this work for JEE-level equations?+
Yes. It handles JEE-level polynomial, trigonometric, logarithmic and exponential equations, including systems and parametric equations. Step-by-step working is on the free plan; guests get one solve per day without signup.
How do I solve a system of two equations with two variables?+
Use substitution (solve one equation for one variable, substitute into the other) or elimination (add or subtract the two equations to cancel a variable). Our dedicated solver for this case is at /solvers/system-of-equations — it shows both methods side by side.
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Next
Related topics to master next
These pair naturally with equation solving — each targets a specific family.
Quadratic Equation Solver
Degree-2 equations — factoring, quadratic formula, completing the square.
Open solver →
Linear Equations Solver
One- and multi-variable linear equations solved step by step.
Open solver →
System of Equations
Two equations, two unknowns — substitution or elimination.
Open solver →
Simultaneous Equations Solver
UK/AU name for systems — same method, AQA/Edexcel/OCR examples.
Open solver →