(12+2x)(24+2x)=640

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Solution for (12+2x)(24+2x)=640 equation: 


Simplifying
(12 + 2x)(24 + 2x) = 640

Multiply (12 + 2x) * (24 + 2x)
(12(24 + 2x) + 2x * (24 + 2x)) = 640
((24 * 12 + 2x * 12) + 2x * (24 + 2x)) = 640
((288 + 24x) + 2x * (24 + 2x)) = 640
(288 + 24x + (24 * 2x + 2x * 2x)) = 640
(288 + 24x + (48x + 4x2)) = 640

Combine like terms: 24x + 48x = 72x
(288 + 72x + 4x2) = 640

Solving
288 + 72x + 4x2 = 640

Solving for variable 'x'.

Reorder the terms:
288 + -640 + 72x + 4x2 = 640 + -640

Combine like terms: 288 + -640 = -352
-352 + 72x + 4x2 = 640 + -640

Combine like terms: 640 + -640 = 0
-352 + 72x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-88 + 18x + x2) = 0

Factor a trinomial.
4((-22 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-22 + -1x)' equal to zero and attempt to solve:

Simplifying
-22 + -1x = 0

Solving
-22 + -1x = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1x = 0 + 22
-1x = 0 + 22

Combine like terms: 0 + 22 = 22
-1x = 22

Divide each side by '-1'.
x = -22

Simplifying
x = -22

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-22, 4}

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