Form: Product Equations A(x)·B(x) = 0
Method: Factor into products and solve each factor
A(x)·B(x) = 0 ⟺ A(x) = 0 or B(x) = 0
x³ - 3x² + 2x = 0
Form: ax⁴ + bx² + c = 0
Method: Let t = x² (t ≥ 0)
Transform to quadratic equation: at² + bt + c = 0
x⁴ - 5x² + 4 = 0
Form: Equations with Substitution Variables
Example: (x² + x)² - 5(x² + x) + 6 = 0
Method: Let t = x² + x, convert to quadratic equation in t
(x² + 2x)² - 7(x² + 2x) + 12 = 0
Form: Symmetric equations
Example: ax⁴ + bx³ + cx² + bx + a = 0
Method: Divide by x² and let t = x + 1/x
x⁴ + 2x³ - x² + 2x + 1 = 0