(16+2x)(24+2x)=180

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Solution for (16+2x)(24+2x)=180 equation: 


Simplifying
(16 + 2x)(24 + 2x) = 180

Multiply (16 + 2x) * (24 + 2x)
(16(24 + 2x) + 2x * (24 + 2x)) = 180
((24 * 16 + 2x * 16) + 2x * (24 + 2x)) = 180
((384 + 32x) + 2x * (24 + 2x)) = 180
(384 + 32x + (24 * 2x + 2x * 2x)) = 180
(384 + 32x + (48x + 4x2)) = 180

Combine like terms: 32x + 48x = 80x
(384 + 80x + 4x2) = 180

Solving
384 + 80x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
384 + -180 + 80x + 4x2 = 180 + -180

Combine like terms: 384 + -180 = 204
204 + 80x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
204 + 80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(51 + 20x + x2) = 0

Factor a trinomial.
4((17 + x)(3 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(17 + x)' equal to zero and attempt to solve:

Simplifying
17 + x = 0

Solving
17 + x = 0

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

Add '-17' to each side of the equation.
17 + -17 + x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + x = 0 + -17
x = 0 + -17

Combine like terms: 0 + -17 = -17
x = -17

Simplifying
x = -17

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-17, -3}

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