(23-2x)(18-2x)=150

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Solution for (23-2x)(18-2x)=150 equation: 


Simplifying
(23 + -2x)(18 + -2x) = 150

Multiply (23 + -2x) * (18 + -2x)
(23(18 + -2x) + -2x * (18 + -2x)) = 150
((18 * 23 + -2x * 23) + -2x * (18 + -2x)) = 150
((414 + -46x) + -2x * (18 + -2x)) = 150
(414 + -46x + (18 * -2x + -2x * -2x)) = 150
(414 + -46x + (-36x + 4x2)) = 150

Combine like terms: -46x + -36x = -82x
(414 + -82x + 4x2) = 150

Solving
414 + -82x + 4x2 = 150

Solving for variable 'x'.

Reorder the terms:
414 + -150 + -82x + 4x2 = 150 + -150

Combine like terms: 414 + -150 = 264
264 + -82x + 4x2 = 150 + -150

Combine like terms: 150 + -150 = 0
264 + -82x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(132 + -41x + 2x2) = 0

Factor a trinomial.
2((4 + -1x)(33 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(33 + -2x)' equal to zero and attempt to solve:

Simplifying
33 + -2x = 0

Solving
33 + -2x = 0

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

Add '-33' to each side of the equation.
33 + -33 + -2x = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -2x = 0 + -33
-2x = 0 + -33

Combine like terms: 0 + -33 = -33
-2x = -33

Divide each side by '-2'.
x = 16.5

Simplifying
x = 16.5
Solution
x = {4, 16.5}

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