15a^2+63a+12=0

Solution for 15a^2+63a+12=0 equation:

Simplifying
15a2 + 63a + 12 = 0

Reorder the terms:
12 + 63a + 15a2 = 0

Solving
12 + 63a + 15a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 21a + 5a2) = 0

Factor a trinomial.
3((4 + a)(1 + 5a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Subproblem 2
Set the factor '(1 + 5a)' equal to zero and attempt to solve:

Simplifying
1 + 5a = 0

Solving
1 + 5a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 5a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5a = 0 + -1
5a = 0 + -1

Combine like terms: 0 + -1 = -1
5a = -1

Divide each side by '5'.
a = -0.2

Simplifying
a = -0.2
Solution
a = {-4, -0.2}