(24+2x)(20+2x)=1596

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Solution for (24+2x)(20+2x)=1596 equation: 


Simplifying
(24 + 2x)(20 + 2x) = 1596

Multiply (24 + 2x) * (20 + 2x)
(24(20 + 2x) + 2x * (20 + 2x)) = 1596
((20 * 24 + 2x * 24) + 2x * (20 + 2x)) = 1596
((480 + 48x) + 2x * (20 + 2x)) = 1596
(480 + 48x + (20 * 2x + 2x * 2x)) = 1596
(480 + 48x + (40x + 4x2)) = 1596

Combine like terms: 48x + 40x = 88x
(480 + 88x + 4x2) = 1596

Solving
480 + 88x + 4x2 = 1596

Solving for variable 'x'.

Reorder the terms:
480 + -1596 + 88x + 4x2 = 1596 + -1596

Combine like terms: 480 + -1596 = -1116
-1116 + 88x + 4x2 = 1596 + -1596

Combine like terms: 1596 + -1596 = 0
-1116 + 88x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-279 + 22x + x2) = 0

Factor a trinomial.
4((-31 + -1x)(9 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-31 + -1x)' equal to zero and attempt to solve:

Simplifying
-31 + -1x = 0

Solving
-31 + -1x = 0

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

Add '31' to each side of the equation.
-31 + 31 + -1x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -1x = 0 + 31
-1x = 0 + 31

Combine like terms: 0 + 31 = 31
-1x = 31

Divide each side by '-1'.
x = -31

Simplifying
x = -31

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-31, 9}

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