120=(4+4x)(6+2x)

Solution for 120=(4+4x)(6+2x) equation:

Simplifying
120 = (4 + 4x)(6 + 2x)

Multiply (4 + 4x) * (6 + 2x)
120 = (4(6 + 2x) + 4x * (6 + 2x))
120 = ((6 * 4 + 2x * 4) + 4x * (6 + 2x))
120 = ((24 + 8x) + 4x * (6 + 2x))
120 = (24 + 8x + (6 * 4x + 2x * 4x))
120 = (24 + 8x + (24x + 8x2))

Combine like terms: 8x + 24x = 32x
120 = (24 + 32x + 8x2)

Solving
120 = 24 + 32x + 8x2

Solving for variable 'x'.

Combine like terms: 120 + -24 = 96
96 + -32x + -8x2 = 24 + 32x + 8x2 + -24 + -32x + -8x2

Reorder the terms:
96 + -32x + -8x2 = 24 + -24 + 32x + -32x + 8x2 + -8x2

Combine like terms: 24 + -24 = 0
96 + -32x + -8x2 = 0 + 32x + -32x + 8x2 + -8x2
96 + -32x + -8x2 = 32x + -32x + 8x2 + -8x2

Combine like terms: 32x + -32x = 0
96 + -32x + -8x2 = 0 + 8x2 + -8x2
96 + -32x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
96 + -32x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(12 + -4x + -1x2) = 0

Factor a trinomial.
8((2 + -1x)(6 + x)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

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

Simplifying
6 + x = 0

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

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

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

Simplifying
x = -6
Solution
x = {2, -6}