(16+2x)*(20+2x)-320=160

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Solution for (16+2x)*(20+2x)-320=160 equation: 


Simplifying
(16 + 2x)(20 + 2x) + -320 = 160

Multiply (16 + 2x) * (20 + 2x)
(16(20 + 2x) + 2x * (20 + 2x)) + -320 = 160
((20 * 16 + 2x * 16) + 2x * (20 + 2x)) + -320 = 160
((320 + 32x) + 2x * (20 + 2x)) + -320 = 160
(320 + 32x + (20 * 2x + 2x * 2x)) + -320 = 160
(320 + 32x + (40x + 4x2)) + -320 = 160

Combine like terms: 32x + 40x = 72x
(320 + 72x + 4x2) + -320 = 160

Reorder the terms:
320 + -320 + 72x + 4x2 = 160

Combine like terms: 320 + -320 = 0
0 + 72x + 4x2 = 160
72x + 4x2 = 160

Solving
72x + 4x2 = 160

Solving for variable 'x'.

Reorder the terms:
-160 + 72x + 4x2 = 160 + -160

Combine like terms: 160 + -160 = 0
-160 + 72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-40 + 18x + x2) = 0

Factor a trinomial.
4((-20 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20

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 = {-20, 2}

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