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

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


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

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

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

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

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

Solving
320 = 192 + 56x + 4x2

Solving for variable 'x'.

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

Reorder the terms:
128 + -56x + -4x2 = 192 + -192 + 56x + -56x + 4x2 + -4x2

Combine like terms: 192 + -192 = 0
128 + -56x + -4x2 = 0 + 56x + -56x + 4x2 + -4x2
128 + -56x + -4x2 = 56x + -56x + 4x2 + -4x2

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(32 + -14x + -1x2) = 0

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

Ignore the factor 4.

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 '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 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 + x = 0 + -16

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

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

Simplifying
x = -16
Solution
x = {2, -16}

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