(2x-6)(x)=108

Solution for (2x-6)(x)=108 equation:

Simplifying
(2x + -6)(x) = 108

Reorder the terms:
(-6 + 2x)(x) = 108

Reorder the terms for easier multiplication:
x(-6 + 2x) = 108
(-6 * x + 2x * x) = 108
(-6x + 2x2) = 108

Solving
-6x + 2x2 = 108

Solving for variable 'x'.

Reorder the terms:
-108 + -6x + 2x2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + -3x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-6, 9}