Write the quadratic equation in standard form: (ax^2+bx+c=0)
If (a=0), solve the linear equation (bx+c=0)
Factor the quadratic (when possible) into ((px+q)(rx+s)=0)
Use the zero-product rule: set each factor equal to 0 and solve
If factoring is not convenient, use the quadratic formula: (x=frac{-bpmsqrt{b^2-4ac}}{2a})
Compute the discriminant: (D=b^2-4ac)
If (D>0), use both (pm) solutions
If (D=0), use (x=frac{-b}{2a})
If (D<0), use complex solutions from the quadratic formula
Simplify the final answers
Check solutions by substituting back into the original equation