Solve the equation 12a3 + 12a2 = - 3a. Show all work.

12a³ + 12a² = - 3a | + 3a

12a³ + 12a² + 3a = 0

3a (4a² + 4a + 1) = 0

3a (2a + 1) ² = 0

3a = 0 or (2a + 1) ² = 0

1) 3a = 0 | : 3

a = 0

2) (2a + 1) ² = 0

2a + 1 = 0 | - 1

2a = - 1 | : 2

a = - 1/2

a ∈ {-1/2, 0}

Used formula:

(a + b) ² = a² + 2ab + b²