(22-2x)(34-2x)=364

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Solution for (22-2x)(34-2x)=364 equation: 


Simplifying
(22 + -2x)(34 + -2x) = 364

Multiply (22 + -2x) * (34 + -2x)
(22(34 + -2x) + -2x * (34 + -2x)) = 364
((34 * 22 + -2x * 22) + -2x * (34 + -2x)) = 364
((748 + -44x) + -2x * (34 + -2x)) = 364
(748 + -44x + (34 * -2x + -2x * -2x)) = 364
(748 + -44x + (-68x + 4x2)) = 364

Combine like terms: -44x + -68x = -112x
(748 + -112x + 4x2) = 364

Solving
748 + -112x + 4x2 = 364

Solving for variable 'x'.

Reorder the terms:
748 + -364 + -112x + 4x2 = 364 + -364

Combine like terms: 748 + -364 = 384
384 + -112x + 4x2 = 364 + -364

Combine like terms: 364 + -364 = 0
384 + -112x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(96 + -28x + x2) = 0

Factor a trinomial.
4((4 + -1x)(24 + -1x)) = 0

Ignore the factor 4.

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 '(24 + -1x)' equal to zero and attempt to solve:

Simplifying
24 + -1x = 0

Solving
24 + -1x = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1x = 0 + -24
-1x = 0 + -24

Combine like terms: 0 + -24 = -24
-1x = -24

Divide each side by '-1'.
x = 24

Simplifying
x = 24
Solution
x = {4, 24}

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