(6x-6)(9x+3)=0

Solution for (6x-6)(9x+3)=0 equation:

Simplifying
(6x + -6)(9x + 3) = 0

Reorder the terms:
(-6 + 6x)(9x + 3) = 0

Reorder the terms:
(-6 + 6x)(3 + 9x) = 0

Multiply (-6 + 6x) * (3 + 9x)
(-6(3 + 9x) + 6x * (3 + 9x)) = 0
((3 * -6 + 9x * -6) + 6x * (3 + 9x)) = 0
((-18 + -54x) + 6x * (3 + 9x)) = 0
(-18 + -54x + (3 * 6x + 9x * 6x)) = 0
(-18 + -54x + (18x + 54x2)) = 0

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

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

Solving for variable 'x'.

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

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

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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
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 = {-0.3333333333, 1}