6a^2+9a-81=0

Solution for 6a^2+9a-81=0 equation:

Simplifying
6a2 + 9a + -81 = 0

Reorder the terms:
-81 + 9a + 6a2 = 0

Solving
-81 + 9a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-27 + 3a + 2a2) = 0

Factor a trinomial.
3((-9 + -2a)(3 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-9 + -2a)' equal to zero and attempt to solve:

Simplifying
-9 + -2a = 0

Solving
-9 + -2a = 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 + -2a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2a = 0 + 9
-2a = 0 + 9

Combine like terms: 0 + 9 = 9
-2a = 9

Divide each side by '-2'.
a = -4.5

Simplifying
a = -4.5
Subproblem 2
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
Solution
a = {-4.5, 3}