(3x-6)(2x-2)=0

Solution for (3x-6)(2x-2)=0 equation:

Simplifying
(3x + -6)(2x + -2) = 0

Reorder the terms:
(-6 + 3x)(2x + -2) = 0

Reorder the terms:
(-6 + 3x)(-2 + 2x) = 0

Multiply (-6 + 3x) * (-2 + 2x)
(-6(-2 + 2x) + 3x * (-2 + 2x)) = 0
((-2 * -6 + 2x * -6) + 3x * (-2 + 2x)) = 0
((12 + -12x) + 3x * (-2 + 2x)) = 0
(12 + -12x + (-2 * 3x + 2x * 3x)) = 0
(12 + -12x + (-6x + 6x2)) = 0

Combine like terms: -12x + -6x = -18x
(12 + -18x + 6x2) = 0

Solving
12 + -18x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + -3x + x2) = 0

Factor a trinomial.
6((1 + -1x)(2 + -1x)) = 0

Ignore the factor 6.
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}