(22+2x)(16+2x)=1080

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Solution for (22+2x)(16+2x)=1080 equation: 


Simplifying
(22 + 2x)(16 + 2x) = 1080

Multiply (22 + 2x) * (16 + 2x)
(22(16 + 2x) + 2x * (16 + 2x)) = 1080
((16 * 22 + 2x * 22) + 2x * (16 + 2x)) = 1080
((352 + 44x) + 2x * (16 + 2x)) = 1080
(352 + 44x + (16 * 2x + 2x * 2x)) = 1080
(352 + 44x + (32x + 4x2)) = 1080

Combine like terms: 44x + 32x = 76x
(352 + 76x + 4x2) = 1080

Solving
352 + 76x + 4x2 = 1080

Solving for variable 'x'.

Reorder the terms:
352 + -1080 + 76x + 4x2 = 1080 + -1080

Combine like terms: 352 + -1080 = -728
-728 + 76x + 4x2 = 1080 + -1080

Combine like terms: 1080 + -1080 = 0
-728 + 76x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-182 + 19x + x2) = 0

Factor a trinomial.
4((-26 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-26 + -1x)' equal to zero and attempt to solve:

Simplifying
-26 + -1x = 0

Solving
-26 + -1x = 0

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

Add '26' to each side of the equation.
-26 + 26 + -1x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -1x = 0 + 26
-1x = 0 + 26

Combine like terms: 0 + 26 = 26
-1x = 26

Divide each side by '-1'.
x = -26

Simplifying
x = -26

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-26, 7}

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