((x+7)(x+7))+8(x+7)+12=0

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Solution for ((x+7)(x+7))+8(x+7)+12=0 equation: 


Simplifying
((x + 7)(x + 7)) + 8(x + 7) + 12 = 0

Reorder the terms:
((7 + x)(x + 7)) + 8(x + 7) + 12 = 0

Reorder the terms:
((7 + x)(7 + x)) + 8(x + 7) + 12 = 0

Multiply (7 + x) * (7 + x)
((7(7 + x) + x(7 + x))) + 8(x + 7) + 12 = 0
(((7 * 7 + x * 7) + x(7 + x))) + 8(x + 7) + 12 = 0
(((49 + 7x) + x(7 + x))) + 8(x + 7) + 12 = 0
((49 + 7x + (7 * x + x * x))) + 8(x + 7) + 12 = 0
((49 + 7x + (7x + x2))) + 8(x + 7) + 12 = 0

Combine like terms: 7x + 7x = 14x
((49 + 14x + x2)) + 8(x + 7) + 12 = 0
(49 + 14x + x2) + 8(x + 7) + 12 = 0

Remove parenthesis around (49 + 14x + x2)
49 + 14x + x2 + 8(x + 7) + 12 = 0

Reorder the terms:
49 + 14x + x2 + 8(7 + x) + 12 = 0
49 + 14x + x2 + (7 * 8 + x * 8) + 12 = 0
49 + 14x + x2 + (56 + 8x) + 12 = 0

Reorder the terms:
49 + 56 + 12 + 14x + 8x + x2 = 0

Combine like terms: 49 + 56 = 105
105 + 12 + 14x + 8x + x2 = 0

Combine like terms: 105 + 12 = 117
117 + 14x + 8x + x2 = 0

Combine like terms: 14x + 8x = 22x
117 + 22x + x2 = 0

Solving
117 + 22x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + x)(9 + x) = 0


Subproblem 1
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 0

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

Add '-13' to each side of the equation.
13 + -13 + x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + x = 0 + -13
x = 0 + -13

Combine like terms: 0 + -13 = -13
x = -13

Simplifying
x = -13

Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {-13, -9}

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