(x-5)(2x-12)=0

Solution for (x-5)(2x-12)=0 equation:

Simplifying
(x + -5)(2x + -12) = 0

Reorder the terms:
(-5 + x)(2x + -12) = 0

Reorder the terms:
(-5 + x)(-12 + 2x) = 0

Multiply (-5 + x) * (-12 + 2x)
(-5(-12 + 2x) + x(-12 + 2x)) = 0
((-12 * -5 + 2x * -5) + x(-12 + 2x)) = 0
((60 + -10x) + x(-12 + 2x)) = 0
(60 + -10x + (-12 * x + 2x * x)) = 0
(60 + -10x + (-12x + 2x2)) = 0

Combine like terms: -10x + -12x = -22x
(60 + -22x + 2x2) = 0

Solving
60 + -22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -11x + x2) = 0

Factor a trinomial.
2((5 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
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
Solution
x = {5, 6}