(x-12)(x-6)=0

Solution for (x-12)(x-6)=0 equation:

Simplifying
(x + -12)(x + -6) = 0

Reorder the terms:
(-12 + x)(x + -6) = 0

Reorder the terms:
(-12 + x)(-6 + x) = 0

Multiply (-12 + x) * (-6 + x)
(-12(-6 + x) + x(-6 + x)) = 0
((-6 * -12 + x * -12) + x(-6 + x)) = 0
((72 + -12x) + x(-6 + x)) = 0
(72 + -12x + (-6 * x + x * x)) = 0
(72 + -12x + (-6x + x2)) = 0

Combine like terms: -12x + -6x = -18x
(72 + -18x + x2) = 0

Solving
72 + -18x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -1x)(12 + -1x) = 0

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {6, 12}