Find all roots: x^3 + 7x^2 + 12x=0

see explanation

Step-by-step explanation:

To find the roots factor the left side

x³ + 7x² + 12x = 0 ← factor out x from each term

x(x² + 7x + 12) = 0

x(x + 3)(x + 4) = 0

Equate each factor to zero and solve for x

x = 0

x + 3 = 0 ⇒ x = - 3

x + 4 = 0 ⇒ x = - 4

Roots are x = - 4, x = - 3, x = 0