(12+2x)(18+2x)=432

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Solution for (12+2x)(18+2x)=432 equation: 


Simplifying
(12 + 2x)(18 + 2x) = 432

Multiply (12 + 2x) * (18 + 2x)
(12(18 + 2x) + 2x * (18 + 2x)) = 432
((18 * 12 + 2x * 12) + 2x * (18 + 2x)) = 432
((216 + 24x) + 2x * (18 + 2x)) = 432
(216 + 24x + (18 * 2x + 2x * 2x)) = 432
(216 + 24x + (36x + 4x2)) = 432

Combine like terms: 24x + 36x = 60x
(216 + 60x + 4x2) = 432

Solving
216 + 60x + 4x2 = 432

Solving for variable 'x'.

Reorder the terms:
216 + -432 + 60x + 4x2 = 432 + -432

Combine like terms: 216 + -432 = -216
-216 + 60x + 4x2 = 432 + -432

Combine like terms: 432 + -432 = 0
-216 + 60x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-54 + 15x + x2) = 0

Factor a trinomial.
4((-18 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18

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 = {-18, 3}

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