(x+9)(x+9)-(-4x-8)(x+8)=

Solution for (x+9)(x+9)-(-4x-8)(x+8)= equation:

Simplifying
(x + 9)(x + 9) + -1(-4x + -8)(x + 8) = 0

Reorder the terms:
(9 + x)(x + 9) + -1(-4x + -8)(x + 8) = 0

Reorder the terms:
(9 + x)(9 + x) + -1(-4x + -8)(x + 8) = 0

Multiply (9 + x) * (9 + x)
(9(9 + x) + x(9 + x)) + -1(-4x + -8)(x + 8) = 0
((9 * 9 + x * 9) + x(9 + x)) + -1(-4x + -8)(x + 8) = 0
((81 + 9x) + x(9 + x)) + -1(-4x + -8)(x + 8) = 0
(81 + 9x + (9 * x + x * x)) + -1(-4x + -8)(x + 8) = 0
(81 + 9x + (9x + x2)) + -1(-4x + -8)(x + 8) = 0

Combine like terms: 9x + 9x = 18x
(81 + 18x + x2) + -1(-4x + -8)(x + 8) = 0

Reorder the terms:
81 + 18x + x2 + -1(-8 + -4x)(x + 8) = 0

Reorder the terms:
81 + 18x + x2 + -1(-8 + -4x)(8 + x) = 0

Multiply (-8 + -4x) * (8 + x)
81 + 18x + x2 + -1(-8(8 + x) + -4x * (8 + x)) = 0
81 + 18x + x2 + -1((8 * -8 + x * -8) + -4x * (8 + x)) = 0
81 + 18x + x2 + -1((-64 + -8x) + -4x * (8 + x)) = 0
81 + 18x + x2 + -1(-64 + -8x + (8 * -4x + x * -4x)) = 0
81 + 18x + x2 + -1(-64 + -8x + (-32x + -4x2)) = 0

Combine like terms: -8x + -32x = -40x
81 + 18x + x2 + -1(-64 + -40x + -4x2) = 0
81 + 18x + x2 + (-64 * -1 + -40x * -1 + -4x2 * -1) = 0
81 + 18x + x2 + (64 + 40x + 4x2) = 0

Reorder the terms:
81 + 64 + 18x + 40x + x2 + 4x2 = 0

Combine like terms: 81 + 64 = 145
145 + 18x + 40x + x2 + 4x2 = 0

Combine like terms: 18x + 40x = 58x
145 + 58x + x2 + 4x2 = 0

Combine like terms: x2 + 4x2 = 5x2
145 + 58x + 5x2 = 0

Solving
145 + 58x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
29 + 11.6x + x2 = 0

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + 11.6x + -29 + x2 = 0 + -29

Reorder the terms:
29 + -29 + 11.6x + x2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + 11.6x + x2 = 0 + -29
11.6x + x2 = 0 + -29

Combine like terms: 0 + -29 = -29
11.6x + x2 = -29

The x term is 11.6x.  Take half its coefficient (5.8).
Square it (33.64) and add it to both sides.

Add '33.64' to each side of the equation.
11.6x + 33.64 + x2 = -29 + 33.64

Reorder the terms:
33.64 + 11.6x + x2 = -29 + 33.64

Combine like terms: -29 + 33.64 = 4.64
33.64 + 11.6x + x2 = 4.64

Factor a perfect square on the left side:
(x + 5.8)(x + 5.8) = 4.64

Calculate the square root of the right side: 2.154065923

Break this problem into two subproblems by setting 
(x + 5.8) equal to 2.154065923 and -2.154065923.

Subproblem 1
x + 5.8 = 2.154065923

Simplifying
x + 5.8 = 2.154065923

Reorder the terms:
5.8 + x = 2.154065923

Solving
5.8 + x = 2.154065923

Solving for variable 'x'.

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

Add '-5.8' to each side of the equation.
5.8 + -5.8 + x = 2.154065923 + -5.8

Combine like terms: 5.8 + -5.8 = 0.0
0.0 + x = 2.154065923 + -5.8
x = 2.154065923 + -5.8

Combine like terms: 2.154065923 + -5.8 = -3.645934077
x = -3.645934077

Simplifying
x = -3.645934077

Subproblem 2
x + 5.8 = -2.154065923

Simplifying
x + 5.8 = -2.154065923

Reorder the terms:
5.8 + x = -2.154065923

Solving
5.8 + x = -2.154065923

Solving for variable 'x'.

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

Add '-5.8' to each side of the equation.
5.8 + -5.8 + x = -2.154065923 + -5.8

Combine like terms: 5.8 + -5.8 = 0.0
0.0 + x = -2.154065923 + -5.8
x = -2.154065923 + -5.8

Combine like terms: -2.154065923 + -5.8 = -7.954065923
x = -7.954065923

Simplifying
x = -7.954065923

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.645934077, -7.954065923}