165=(20-2x)(24-2x)

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Solution for 165=(20-2x)(24-2x) equation:


Simplifying
165 = (20 + -2x)(24 + -2x)

Multiply (20 + -2x) * (24 + -2x)
165 = (20(24 + -2x) + -2x * (24 + -2x))
165 = ((24 * 20 + -2x * 20) + -2x * (24 + -2x))
165 = ((480 + -40x) + -2x * (24 + -2x))
165 = (480 + -40x + (24 * -2x + -2x * -2x))
165 = (480 + -40x + (-48x + 4x2))

Combine like terms: -40x + -48x = -88x
165 = (480 + -88x + 4x2)

Solving
165 = 480 + -88x + 4x2

Solving for variable 'x'.

Combine like terms: 165 + -480 = -315
-315 + 88x + -4x2 = 480 + -88x + 4x2 + -480 + 88x + -4x2

Reorder the terms:
-315 + 88x + -4x2 = 480 + -480 + -88x + 88x + 4x2 + -4x2

Combine like terms: 480 + -480 = 0
-315 + 88x + -4x2 = 0 + -88x + 88x + 4x2 + -4x2
-315 + 88x + -4x2 = -88x + 88x + 4x2 + -4x2

Combine like terms: -88x + 88x = 0
-315 + 88x + -4x2 = 0 + 4x2 + -4x2
-315 + 88x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-315 + 88x + -4x2 = 0

Factor a trinomial.
(-35 + 2x)(9 + -2x) = 0


Subproblem 1
Set the factor '(-35 + 2x)' equal to zero and attempt to solve:

Simplifying
-35 + 2x = 0

Solving
-35 + 2x = 0

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

Add '35' to each side of the equation.
-35 + 35 + 2x = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 2x = 0 + 35
2x = 0 + 35

Combine like terms: 0 + 35 = 35
2x = 35

Divide each side by '2'.
x = 17.5

Simplifying
x = 17.5

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {17.5, 4.5}

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