(12+2x)(20+2x)=468

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Solution for (12+2x)(20+2x)=468 equation: 


Simplifying
(12 + 2x)(20 + 2x) = 468

Multiply (12 + 2x) * (20 + 2x)
(12(20 + 2x) + 2x * (20 + 2x)) = 468
((20 * 12 + 2x * 12) + 2x * (20 + 2x)) = 468
((240 + 24x) + 2x * (20 + 2x)) = 468
(240 + 24x + (20 * 2x + 2x * 2x)) = 468
(240 + 24x + (40x + 4x2)) = 468

Combine like terms: 24x + 40x = 64x
(240 + 64x + 4x2) = 468

Solving
240 + 64x + 4x2 = 468

Solving for variable 'x'.

Reorder the terms:
240 + -468 + 64x + 4x2 = 468 + -468

Combine like terms: 240 + -468 = -228
-228 + 64x + 4x2 = 468 + -468

Combine like terms: 468 + -468 = 0
-228 + 64x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-57 + 16x + x2) = 0

Factor a trinomial.
4((-19 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-19 + -1x)' equal to zero and attempt to solve:

Simplifying
-19 + -1x = 0

Solving
-19 + -1x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1x = 0 + 19
-1x = 0 + 19

Combine like terms: 0 + 19 = 19
-1x = 19

Divide each side by '-1'.
x = -19

Simplifying
x = -19

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-19, 3}

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