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

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

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

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

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

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

Combine like terms: -6x + -12x = -18x
0 = (36 + -18x + 2x2)

Solving
0 = 36 + -18x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -36 = -36
-36 + 18x + -2x2 = 36 + -18x + 2x2 + -36 + 18x + -2x2

Reorder the terms:
-36 + 18x + -2x2 = 36 + -36 + -18x + 18x + 2x2 + -2x2

Combine like terms: 36 + -36 = 0
-36 + 18x + -2x2 = 0 + -18x + 18x + 2x2 + -2x2
-36 + 18x + -2x2 = -18x + 18x + 2x2 + -2x2

Combine like terms: -18x + 18x = 0
-36 + 18x + -2x2 = 0 + 2x2 + -2x2
-36 + 18x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-36 + 18x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 9x + -1x2) = 0

Factor a trinomial.
2((-6 + x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {6, 3}