(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((3 + -1x)(17 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 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 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

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

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