(12+2x)(8+2x)-192=0

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Solution for (12+2x)(8+2x)-192=0 equation: 


Simplifying
(12 + 2x)(8 + 2x) + -192 = 0

Multiply (12 + 2x) * (8 + 2x)
(12(8 + 2x) + 2x * (8 + 2x)) + -192 = 0
((8 * 12 + 2x * 12) + 2x * (8 + 2x)) + -192 = 0
((96 + 24x) + 2x * (8 + 2x)) + -192 = 0
(96 + 24x + (8 * 2x + 2x * 2x)) + -192 = 0
(96 + 24x + (16x + 4x2)) + -192 = 0

Combine like terms: 24x + 16x = 40x
(96 + 40x + 4x2) + -192 = 0

Reorder the terms:
96 + -192 + 40x + 4x2 = 0

Combine like terms: 96 + -192 = -96
-96 + 40x + 4x2 = 0

Solving
-96 + 40x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + 10x + x2) = 0

Factor a trinomial.
4((-12 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

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}

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