(x+8)(x+8)+9(x+8)+8=0

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Solution for (x+8)(x+8)+9(x+8)+8=0 equation: 


Simplifying
(x + 8)(x + 8) + 9(x + 8) + 8 = 0

Reorder the terms:
(8 + x)(x + 8) + 9(x + 8) + 8 = 0

Reorder the terms:
(8 + x)(8 + x) + 9(x + 8) + 8 = 0

Multiply (8 + x) * (8 + x)
(8(8 + x) + x(8 + x)) + 9(x + 8) + 8 = 0
((8 * 8 + x * 8) + x(8 + x)) + 9(x + 8) + 8 = 0
((64 + 8x) + x(8 + x)) + 9(x + 8) + 8 = 0
(64 + 8x + (8 * x + x * x)) + 9(x + 8) + 8 = 0
(64 + 8x + (8x + x2)) + 9(x + 8) + 8 = 0

Combine like terms: 8x + 8x = 16x
(64 + 16x + x2) + 9(x + 8) + 8 = 0

Reorder the terms:
64 + 16x + x2 + 9(8 + x) + 8 = 0
64 + 16x + x2 + (8 * 9 + x * 9) + 8 = 0
64 + 16x + x2 + (72 + 9x) + 8 = 0

Reorder the terms:
64 + 72 + 8 + 16x + 9x + x2 = 0

Combine like terms: 64 + 72 = 136
136 + 8 + 16x + 9x + x2 = 0

Combine like terms: 136 + 8 = 144
144 + 16x + 9x + x2 = 0

Combine like terms: 16x + 9x = 25x
144 + 25x + x2 = 0

Solving
144 + 25x + x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16

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 = {-16, -9}

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