(2x+16)(2x+12)=320

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Solution for (2x+16)(2x+12)=320 equation: 


Simplifying
(2x + 16)(2x + 12) = 320

Reorder the terms:
(16 + 2x)(2x + 12) = 320

Reorder the terms:
(16 + 2x)(12 + 2x) = 320

Multiply (16 + 2x) * (12 + 2x)
(16(12 + 2x) + 2x * (12 + 2x)) = 320
((12 * 16 + 2x * 16) + 2x * (12 + 2x)) = 320
((192 + 32x) + 2x * (12 + 2x)) = 320
(192 + 32x + (12 * 2x + 2x * 2x)) = 320
(192 + 32x + (24x + 4x2)) = 320

Combine like terms: 32x + 24x = 56x
(192 + 56x + 4x2) = 320

Solving
192 + 56x + 4x2 = 320

Solving for variable 'x'.

Reorder the terms:
192 + -320 + 56x + 4x2 = 320 + -320

Combine like terms: 192 + -320 = -128
-128 + 56x + 4x2 = 320 + -320

Combine like terms: 320 + -320 = 0
-128 + 56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-32 + 14x + x2) = 0

Factor a trinomial.
4((-16 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16

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 = {-16, 2}

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