-8x(x+5)=-168

Solution for -8x(x+5)=-168 equation:

Simplifying
-8x(x + 5) = -168

Reorder the terms:
-8x(5 + x) = -168
(5 * -8x + x * -8x) = -168
(-40x + -8x2) = -168

Solving
-40x + -8x2 = -168

Solving for variable 'x'.

Reorder the terms:
168 + -40x + -8x2 = -168 + 168

Combine like terms: -168 + 168 = 0
168 + -40x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(21 + -5x + -1x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(21 + -5x + -1x2)' equal to zero and attempt to solve:

Simplifying
21 + -5x + -1x2 = 0

Solving
21 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-21 + 5x + x2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 5x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 5x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 5x + x2 = 0 + 21
5x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
5x + x2 = 21

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 21 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 21 + 6.25

Combine like terms: 21 + 6.25 = 27.25
6.25 + 5x + x2 = 27.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
x + 2.5 = 5.220153254

Simplifying
x + 2.5 = 5.220153254

Reorder the terms:
2.5 + x = 5.220153254

Solving
2.5 + x = 5.220153254

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 5.220153254 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.220153254 + -2.5
x = 5.220153254 + -2.5

Combine like terms: 5.220153254 + -2.5 = 2.720153254
x = 2.720153254

Simplifying
x = 2.720153254

Subproblem 2
x + 2.5 = -5.220153254

Simplifying
x + 2.5 = -5.220153254

Reorder the terms:
2.5 + x = -5.220153254

Solving
2.5 + x = -5.220153254

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -5.220153254 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.220153254 + -2.5
x = -5.220153254 + -2.5

Combine like terms: -5.220153254 + -2.5 = -7.720153254
x = -7.720153254

Simplifying
x = -7.720153254

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.720153254, -7.720153254}
Solution
x = {2.720153254, -7.720153254}