252=(2x+12)(2x+16)

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Solution for 252=(2x+12)(2x+16) equation: 


Simplifying
252 = (2x + 12)(2x + 16)

Reorder the terms:
252 = (12 + 2x)(2x + 16)

Reorder the terms:
252 = (12 + 2x)(16 + 2x)

Multiply (12 + 2x) * (16 + 2x)
252 = (12(16 + 2x) + 2x * (16 + 2x))
252 = ((16 * 12 + 2x * 12) + 2x * (16 + 2x))
252 = ((192 + 24x) + 2x * (16 + 2x))
252 = (192 + 24x + (16 * 2x + 2x * 2x))
252 = (192 + 24x + (32x + 4x2))

Combine like terms: 24x + 32x = 56x
252 = (192 + 56x + 4x2)

Solving
252 = 192 + 56x + 4x2

Solving for variable 'x'.

Combine like terms: 252 + -192 = 60
60 + -56x + -4x2 = 192 + 56x + 4x2 + -192 + -56x + -4x2

Reorder the terms:
60 + -56x + -4x2 = 192 + -192 + 56x + -56x + 4x2 + -4x2

Combine like terms: 192 + -192 = 0
60 + -56x + -4x2 = 0 + 56x + -56x + 4x2 + -4x2
60 + -56x + -4x2 = 56x + -56x + 4x2 + -4x2

Combine like terms: 56x + -56x = 0
60 + -56x + -4x2 = 0 + 4x2 + -4x2
60 + -56x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
60 + -56x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + -14x + -1x2) = 0

Factor a trinomial.
4((1 + -1x)(15 + x)) = 0

Ignore the factor 4.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15
Solution
x = {1, -15}

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