(2x+16)(2x+24)=1140

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Solution for (2x+16)(2x+24)=1140 equation: 


Simplifying
(2x + 16)(2x + 24) = 1140

Reorder the terms:
(16 + 2x)(2x + 24) = 1140

Reorder the terms:
(16 + 2x)(24 + 2x) = 1140

Multiply (16 + 2x) * (24 + 2x)
(16(24 + 2x) + 2x * (24 + 2x)) = 1140
((24 * 16 + 2x * 16) + 2x * (24 + 2x)) = 1140
((384 + 32x) + 2x * (24 + 2x)) = 1140
(384 + 32x + (24 * 2x + 2x * 2x)) = 1140
(384 + 32x + (48x + 4x2)) = 1140

Combine like terms: 32x + 48x = 80x
(384 + 80x + 4x2) = 1140

Solving
384 + 80x + 4x2 = 1140

Solving for variable 'x'.

Reorder the terms:
384 + -1140 + 80x + 4x2 = 1140 + -1140

Combine like terms: 384 + -1140 = -756
-756 + 80x + 4x2 = 1140 + -1140

Combine like terms: 1140 + -1140 = 0
-756 + 80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-189 + 20x + x2) = 0

Factor a trinomial.
4((-27 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-27 + -1x)' equal to zero and attempt to solve:

Simplifying
-27 + -1x = 0

Solving
-27 + -1x = 0

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

Add '27' to each side of the equation.
-27 + 27 + -1x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1x = 0 + 27
-1x = 0 + 27

Combine like terms: 0 + 27 = 27
-1x = 27

Divide each side by '-1'.
x = -27

Simplifying
x = -27

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 = {-27, 7}

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