(2x-4)(x)=96

Solution for (2x-4)(x)=96 equation:

Simplifying
(2x + -4)(x) = 96

Reorder the terms:
(-4 + 2x)(x) = 96

Reorder the terms for easier multiplication:
x(-4 + 2x) = 96
(-4 * x + 2x * x) = 96
(-4x + 2x2) = 96

Solving
-4x + 2x2 = 96

Solving for variable 'x'.

Reorder the terms:
-96 + -4x + 2x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-96 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + -2x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-6, 8}