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

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


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

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

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

Solving
180 = 384 + -80x + 4x2

Solving for variable 'x'.

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

Reorder the terms:
-204 + 80x + -4x2 = 384 + -384 + -80x + 80x + 4x2 + -4x2

Combine like terms: 384 + -384 = 0
-204 + 80x + -4x2 = 0 + -80x + 80x + 4x2 + -4x2
-204 + 80x + -4x2 = -80x + 80x + 4x2 + -4x2

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(-51 + 20x + -1x2) = 0

Factor a trinomial.
4((-17 + x)(3 + -1x)) = 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 + -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
Solution
x = {17, 3}

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