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

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


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

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

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

Solving
396 = 192 + 56x + 4x2

Solving for variable 'x'.

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

Reorder the terms:
204 + -56x + -4x2 = 192 + -192 + 56x + -56x + 4x2 + -4x2

Combine like terms: 192 + -192 = 0
204 + -56x + -4x2 = 0 + 56x + -56x + 4x2 + -4x2
204 + -56x + -4x2 = 56x + -56x + 4x2 + -4x2

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(51 + -14x + -1x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(17 + x)' equal to zero and attempt to solve:

Simplifying
17 + x = 0

Solving
17 + x = 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 + x = 0 + -17

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

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

Simplifying
x = -17
Solution
x = {3, -17}

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