Algebra guide
Solving Linear, Quadratic, and Polynomial Equations
Use inverse operations, factoring, and the quadratic formula while checking every proposed solution.
9 min readBeginnerUpdated 2026-07-12
What you will learn
- Isolate a variable with equivalent operations
- Choose a quadratic method
- Check solutions in the original equation
Concept 1
Keep an equation balanced
Apply the same reversible operation to both sides. Combine like terms before moving terms, and delay division when it would introduce fractions unnecessarily.
Concept 2
Put quadratics in standard form
Move every term to one side so the equation equals zero. Then factor, complete the square, or use the quadratic formula.
Concept 3
The discriminant predicts the roots
The value b²−4ac tells whether a real quadratic has two, one, or no real roots.
Worked example
Solve x²−5x+6=0
- 1Find two numbers that multiply to 6 and add to −5: −2 and −3.
- 2Factor as (x−2)(x−3)=0.
- 3Set each factor equal to zero.
Answer
Common mistakes
- Changing only one side of the equation
- Dividing by an expression that might be zero
- Failing to check extraneous solutions
Check your understanding