9a^2x^2-12ax-12=0

Solution for 9a^2x^2-12ax-12=0 equation:

Simplifying
9a2x2 + -12ax + -12 = 0

Reorder the terms:
-12 + -12ax + 9a2x2 = 0

Solving
-12 + -12ax + 9a2x2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -4ax + 3a2x2) = 0

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

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

Simplifying
-2 + -3ax = 0

Solving
-2 + -3ax = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3ax = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3ax = 0 + 2
-3ax = 0 + 2

Combine like terms: 0 + 2 = 2
-3ax = 2

Divide each side by '-3x'.
a = -0.6666666667x-1

Simplifying
a = -0.6666666667x-1
Subproblem 2
Set the factor '(2 + -1ax)' equal to zero and attempt to solve:

Simplifying
2 + -1ax = 0

Solving
2 + -1ax = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1ax = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1ax = 0 + -2
-1ax = 0 + -2

Combine like terms: 0 + -2 = -2
-1ax = -2

Divide each side by '-1x'.
a = 2x-1

Simplifying
a = 2x-1
Solution
a = {-0.6666666667x-1, 2x-1}