15a^2+63a-162=0

Solution for 15a^2+63a-162=0 equation:

Simplifying
15a2 + 63a + -162 = 0

Reorder the terms:
-162 + 63a + 15a2 = 0

Solving
-162 + 63a + 15a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-54 + 21a + 5a2) = 0

Factor a trinomial.
3((-6 + -1a)(9 + -5a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(9 + -5a)' equal to zero and attempt to solve:

Simplifying
9 + -5a = 0

Solving
9 + -5a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5a = 0 + -9
-5a = 0 + -9

Combine like terms: 0 + -9 = -9
-5a = -9

Divide each side by '-5'.
a = 1.8

Simplifying
a = 1.8
Solution
a = {-6, 1.8}