(14+2x)(22+2x)=884

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Solution for (14+2x)(22+2x)=884 equation: 


Simplifying
(14 + 2x)(22 + 2x) = 884

Multiply (14 + 2x) * (22 + 2x)
(14(22 + 2x) + 2x * (22 + 2x)) = 884
((22 * 14 + 2x * 14) + 2x * (22 + 2x)) = 884
((308 + 28x) + 2x * (22 + 2x)) = 884
(308 + 28x + (22 * 2x + 2x * 2x)) = 884
(308 + 28x + (44x + 4x2)) = 884

Combine like terms: 28x + 44x = 72x
(308 + 72x + 4x2) = 884

Solving
308 + 72x + 4x2 = 884

Solving for variable 'x'.

Reorder the terms:
308 + -884 + 72x + 4x2 = 884 + -884

Combine like terms: 308 + -884 = -576
-576 + 72x + 4x2 = 884 + -884

Combine like terms: 884 + -884 = 0
-576 + 72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-144 + 18x + x2) = 0

Factor a trinomial.
4((-24 + -1x)(6 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-24, 6}

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