(x-4)(x+3)(2)=120

Solution for (x-4)(x+3)(2)=120 equation:

Simplifying
(x + -4)(x + 3)(2) = 120

Reorder the terms:
(-4 + x)(x + 3)(2) = 120

Reorder the terms:
(-4 + x)(3 + x)(2) = 120

Reorder the terms for easier multiplication:
2(-4 + x)(3 + x) = 120

Multiply (-4 + x) * (3 + x)
2(-4(3 + x) + x(3 + x)) = 120
2((3 * -4 + x * -4) + x(3 + x)) = 120
2((-12 + -4x) + x(3 + x)) = 120
2(-12 + -4x + (3 * x + x * x)) = 120
2(-12 + -4x + (3x + x2)) = 120

Combine like terms: -4x + 3x = -1x
2(-12 + -1x + x2) = 120
(-12 * 2 + -1x * 2 + x2 * 2) = 120
(-24 + -2x + 2x2) = 120

Solving
-24 + -2x + 2x2 = 120

Solving for variable 'x'.

Reorder the terms:
-24 + -120 + -2x + 2x2 = 120 + -120

Combine like terms: -24 + -120 = -144
-144 + -2x + 2x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-144 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + -1x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-8, 9}