Equation Solver: How to Solve Linear, Quadratic, and Systems of Equations Step by Step

Stuck on a linear equation, a quadratic, or a system with two unknowns? An equation solver shows you the answer and the steps to get there — useful for checking homework, preparing for exams, or verifying your own work before you submit it. Knowing how the solving process works matters too, so you’re not blindly trusting a result.

Try our free Equation Solver — enter any equation and get the solution with step-by-step working in seconds.

Step 1: Identify the Type of Equation

Before solving, recognize what you’re dealing with:

• Linear equations — no exponents, e.g. 2x + 5 = 11. Solution is a straight line on a graph.
• Quadratic equations — terms like x², e.g. x² - 5x + 6 = 0. Graph is a parabola.
• Systems of equations — two or more equations with multiple variables, e.g. y = 2x + 1 and y = -x + 4.
• Polynomial, rational, exponential, logarithmic — each has its own solving strategy.

Step 2: Isolate the Variable

For linear equations, rearrange terms so the variable ends up alone on one side. Add or subtract the same value from both sides, then multiply or divide to simplify. For example, in 2x + 5 = 11: subtract 5 from both sides to get 2x = 6, then divide by 2 to get x = 3.

Step 3: Apply the Right Method

Each equation type needs a different approach:

• Quadratics: Factoring, completing the square, or the quadratic formula x = (-b ± √(b² - 4ac)) / 2a.
• Systems: Substitution (solve one equation for a variable, plug into the other) or elimination (add/subtract equations to cancel a variable).
• Rational equations: Multiply through by the common denominator to clear fractions.
• Exponentials/logs: Take the log of both sides, or exponentiate to undo a log.

Step 4: Check Your Answer

Plug the solution back into the original equation. If both sides balance, you’re correct. This is where a solver earns its keep — paste your equation into the Equation Solver, compare the answer with your work, and review the step-by-step breakdown if you went wrong.

Common Mistakes to Avoid

• Forgetting to flip signs when moving terms across the equals sign.
• Losing the ± sign when taking square roots — quadratic equations have two solutions.
• Dropping a solution in rational equations when a denominator becomes zero (that value is invalid).
• Arithmetic slips in the quadratic formula — double-check b² - 4ac before dividing.

Whether you’re a student grinding through homework or a professional double-checking calculations, the Equation Solver gives you the answer and the steps — so you learn the method, not just the result.