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

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

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

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

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

Multiply (-6 + 3x) * (-6 + 6x)
(-6(-6 + 6x) + 3x * (-6 + 6x)) = 0
((-6 * -6 + 6x * -6) + 3x * (-6 + 6x)) = 0
((36 + -36x) + 3x * (-6 + 6x)) = 0
(36 + -36x + (-6 * 3x + 6x * 3x)) = 0
(36 + -36x + (-18x + 18x2)) = 0

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

Solving
36 + -54x + 18x2 = 0

Solving for variable 'x'.

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

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

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

Simplifying
x = 2
Solution
x = {1, 2}