(24+2x)(14+2x)=816

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Solution for (24+2x)(14+2x)=816 equation: 


Simplifying
(24 + 2x)(14 + 2x) = 816

Multiply (24 + 2x) * (14 + 2x)
(24(14 + 2x) + 2x * (14 + 2x)) = 816
((14 * 24 + 2x * 24) + 2x * (14 + 2x)) = 816
((336 + 48x) + 2x * (14 + 2x)) = 816
(336 + 48x + (14 * 2x + 2x * 2x)) = 816
(336 + 48x + (28x + 4x2)) = 816

Combine like terms: 48x + 28x = 76x
(336 + 76x + 4x2) = 816

Solving
336 + 76x + 4x2 = 816

Solving for variable 'x'.

Reorder the terms:
336 + -816 + 76x + 4x2 = 816 + -816

Combine like terms: 336 + -816 = -480
-480 + 76x + 4x2 = 816 + -816

Combine like terms: 816 + -816 = 0
-480 + 76x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-120 + 19x + x2) = 0

Factor a trinomial.
4((-24 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-24, 5}

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