(12+2x)(16+2x)=396

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Solution for (12+2x)(16+2x)=396 equation: 


Simplifying
(12 + 2x)(16 + 2x) = 396

Multiply (12 + 2x) * (16 + 2x)
(12(16 + 2x) + 2x * (16 + 2x)) = 396
((16 * 12 + 2x * 12) + 2x * (16 + 2x)) = 396
((192 + 24x) + 2x * (16 + 2x)) = 396
(192 + 24x + (16 * 2x + 2x * 2x)) = 396
(192 + 24x + (32x + 4x2)) = 396

Combine like terms: 24x + 32x = 56x
(192 + 56x + 4x2) = 396

Solving
192 + 56x + 4x2 = 396

Solving for variable 'x'.

Reorder the terms:
192 + -396 + 56x + 4x2 = 396 + -396

Combine like terms: 192 + -396 = -204
-204 + 56x + 4x2 = 396 + -396

Combine like terms: 396 + -396 = 0
-204 + 56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-51 + 14x + x2) = 0

Factor a trinomial.
4((-17 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17

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 = {-17, 3}

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