3a^2-27a-108=0

Solution for 3a^2-27a-108=0 equation:

Simplifying
3a2 + -27a + -108 = 0

Reorder the terms:
-108 + -27a + 3a2 = 0

Solving
-108 + -27a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-36 + -9a + a2) = 0

Factor a trinomial.
3((-3 + -1a)(12 + -1a)) = 0

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

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1a = 0 + -12
-1a = 0 + -12

Combine like terms: 0 + -12 = -12
-1a = -12

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {-3, 12}