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

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

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

Multiply (6 + -2x) * (6 + -6x)
0 = (6(6 + -6x) + -2x * (6 + -6x))
0 = ((6 * 6 + -6x * 6) + -2x * (6 + -6x))
0 = ((36 + -36x) + -2x * (6 + -6x))
0 = (36 + -36x + (6 * -2x + -6x * -2x))
0 = (36 + -36x + (-12x + 12x2))

Combine like terms: -36x + -12x = -48x
0 = (36 + -48x + 12x2)

Solving
0 = 36 + -48x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + -36 = -36
-36 + 48x + -12x2 = 36 + -48x + 12x2 + -36 + 48x + -12x2

Reorder the terms:
-36 + 48x + -12x2 = 36 + -36 + -48x + 48x + 12x2 + -12x2

Combine like terms: 36 + -36 = 0
-36 + 48x + -12x2 = 0 + -48x + 48x + 12x2 + -12x2
-36 + 48x + -12x2 = -48x + 48x + 12x2 + -12x2

Combine like terms: -48x + 48x = 0
-36 + 48x + -12x2 = 0 + 12x2 + -12x2
-36 + 48x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-36 + 48x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-3 + 4x + -1x2) = 0

Factor a trinomial.
12((-3 + x)(1 + -1x)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

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

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

Simplifying
x = 3
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 = {3, 1}