15a^2-3a-12=0

Solution for 15a^2-3a-12=0 equation:

Simplifying
15a2 + -3a + -12 = 0

Reorder the terms:
-12 + -3a + 15a2 = 0

Solving
-12 + -3a + 15a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -1a + 5a2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -5a)' equal to zero and attempt to solve:

Simplifying
-4 + -5a = 0

Solving
-4 + -5a = 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 + -5a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5a = 0 + 4
-5a = 0 + 4

Combine like terms: 0 + 4 = 4
-5a = 4

Divide each side by '-5'.
a = -0.8

Simplifying
a = -0.8
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 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 + -1a = 0 + -1

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

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

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {-0.8, 1}