Set the equation equal to zero
Simplify and combine like terms
Factor out the greatest common factor
Use factoring methods
Apply the zero product property
Check for special patterns
Use substitution when appropriate
Use the Rational Root Theorem
Test possible rational roots
Divide out found factors using synthetic division or polynomial long division
Solve the remaining lower-degree equation
Use the quadratic formula for degree 2 factors
Use completing the square when helpful
Use the cubic or quartic formulas when needed
Use graphing to estimate real roots
Use numerical methods for difficult equations
Verify all solutions in the original equation
Reject any extraneous solutions