(6x-6)(9x+6)=0

Solution for (6x-6)(9x+6)=0 equation:

Simplifying
(6x + -6)(9x + 6) = 0

Reorder the terms:
(-6 + 6x)(9x + 6) = 0

Reorder the terms:
(-6 + 6x)(6 + 9x) = 0

Multiply (-6 + 6x) * (6 + 9x)
(-6(6 + 9x) + 6x * (6 + 9x)) = 0
((6 * -6 + 9x * -6) + 6x * (6 + 9x)) = 0
((-36 + -54x) + 6x * (6 + 9x)) = 0
(-36 + -54x + (6 * 6x + 9x * 6x)) = 0
(-36 + -54x + (36x + 54x2)) = 0

Combine like terms: -54x + 36x = -18x
(-36 + -18x + 54x2) = 0

Solving
-36 + -18x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18'.
18(-2 + -1x + 3x2) = 0

Factor a trinomial.
18((-2 + -3x)(1 + -1x)) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

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

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

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

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

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

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