(22+2x)(12+2x)=504

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Solution for (22+2x)(12+2x)=504 equation: 


Simplifying
(22 + 2x)(12 + 2x) = 504

Multiply (22 + 2x) * (12 + 2x)
(22(12 + 2x) + 2x * (12 + 2x)) = 504
((12 * 22 + 2x * 22) + 2x * (12 + 2x)) = 504
((264 + 44x) + 2x * (12 + 2x)) = 504
(264 + 44x + (12 * 2x + 2x * 2x)) = 504
(264 + 44x + (24x + 4x2)) = 504

Combine like terms: 44x + 24x = 68x
(264 + 68x + 4x2) = 504

Solving
264 + 68x + 4x2 = 504

Solving for variable 'x'.

Reorder the terms:
264 + -504 + 68x + 4x2 = 504 + -504

Combine like terms: 264 + -504 = -240
-240 + 68x + 4x2 = 504 + -504

Combine like terms: 504 + -504 = 0
-240 + 68x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-60 + 17x + x2) = 0

Factor a trinomial.
4((-20 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20

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 = {-20, 3}

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