3a^2-3a-81=9

Solution for 3a^2-3a-81=9 equation:

Simplifying
3a2 + -3a + -81 = 9

Reorder the terms:
-81 + -3a + 3a2 = 9

Solving
-81 + -3a + 3a2 = 9

Solving for variable 'a'.

Reorder the terms:
-81 + -9 + -3a + 3a2 = 9 + -9

Combine like terms: -81 + -9 = -90
-90 + -3a + 3a2 = 9 + -9

Combine like terms: 9 + -9 = 0
-90 + -3a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + -1a + a2) = 0

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

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

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = -5

Simplifying
a = -5
Subproblem 2
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
Solution
a = {-5, 6}