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

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


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

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

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

Solving
480 + -88x + 4x2 = 165

Solving for variable 'x'.

Reorder the terms:
480 + -165 + -88x + 4x2 = 165 + -165

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

Combine like terms: 165 + -165 = 0
315 + -88x + 4x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {4.5, 17.5}

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