[(16+2x)(8+2x)]-(8*16)=0

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Solution for [(16+2x)(8+2x)]-(8*16)=0 equation: 


Simplifying
[(16 + 2x)(8 + 2x)] + -1(8 * 16) = 0

Multiply (16 + 2x) * (8 + 2x)
[(16(8 + 2x) + 2x * (8 + 2x))] + -1(8 * 16) = 0
[((8 * 16 + 2x * 16) + 2x * (8 + 2x))] + -1(8 * 16) = 0
[((128 + 32x) + 2x * (8 + 2x))] + -1(8 * 16) = 0
[(128 + 32x + (8 * 2x + 2x * 2x))] + -1(8 * 16) = 0
[(128 + 32x + (16x + 4x2))] + -1(8 * 16) = 0

Combine like terms: 32x + 16x = 48x
[(128 + 48x + 4x2)] + -1(8 * 16) = 0
[128 + 48x + 4x2] + -1(8 * 16) = 0

Remove brackets around [128 + 48x + 4x2]
128 + 48x + 4x2 + -1(8 * 16) = 0

Multiply 8 * 16
128 + 48x + 4x2 + -1(128) = 0

Multiply -1 * 128
128 + 48x + 4x2 + -128 = 0

Reorder the terms:
128 + -128 + 48x + 4x2 = 0

Combine like terms: 128 + -128 = 0
0 + 48x + 4x2 = 0
48x + 4x2 = 0

Solving
48x + 4x2 = 0

Solving for variable 'x'.

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

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
12 + x = 0

Solving
12 + x = 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 + x = 0 + -12

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

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

Simplifying
x = -12
Solution
x = {0, -12}

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