Question

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

Answer 1

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