(12+2x)(4+x)=96

Solution for (12+2x)(4+x)=96 equation:

Simplifying
(12 + 2x)(4 + x) = 96

Multiply (12 + 2x) * (4 + x)
(12(4 + x) + 2x * (4 + x)) = 96
((4 * 12 + x * 12) + 2x * (4 + x)) = 96
((48 + 12x) + 2x * (4 + x)) = 96
(48 + 12x + (4 * 2x + x * 2x)) = 96
(48 + 12x + (8x + 2x2)) = 96

Combine like terms: 12x + 8x = 20x
(48 + 20x + 2x2) = 96

Solving
48 + 20x + 2x2 = 96

Solving for variable 'x'.

Reorder the terms:
48 + -96 + 20x + 2x2 = 96 + -96

Combine like terms: 48 + -96 = -48
-48 + 20x + 2x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-48 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 10x + x2) = 0

Factor a trinomial.
2((-12 + -1x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
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
Solution
x = {-12, 2}