-6(x+5)8x=2(x+5)-8

Solution for -6(x+5)8x=2(x+5)-8 equation:

Simplifying
-6(x + 5) * 8x = 2(x + 5) + -8

Reorder the terms:
-6(5 + x) * 8x = 2(x + 5) + -8

Reorder the terms for easier multiplication:
-6 * 8x(5 + x) = 2(x + 5) + -8

Multiply -6 * 8
-48x(5 + x) = 2(x + 5) + -8
(5 * -48x + x * -48x) = 2(x + 5) + -8
(-240x + -48x2) = 2(x + 5) + -8

Reorder the terms:
-240x + -48x2 = 2(5 + x) + -8
-240x + -48x2 = (5 * 2 + x * 2) + -8
-240x + -48x2 = (10 + 2x) + -8

Reorder the terms:
-240x + -48x2 = 10 + -8 + 2x

Combine like terms: 10 + -8 = 2
-240x + -48x2 = 2 + 2x

Solving
-240x + -48x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
-2 + -240x + -2x + -48x2 = 2 + 2x + -2 + -2x

Combine like terms: -240x + -2x = -242x
-2 + -242x + -48x2 = 2 + 2x + -2 + -2x

Reorder the terms:
-2 + -242x + -48x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
-2 + -242x + -48x2 = 0 + 2x + -2x
-2 + -242x + -48x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-2 + -242x + -48x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 121x + 24x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(1 + 121x + 24x2)' equal to zero and attempt to solve:

Simplifying
1 + 121x + 24x2 = 0

Solving
1 + 121x + 24x2 = 0

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

Divide each side by '24'.
0.04166666667 + 5.041666667x + x2 = 0

Move the constant term to the right:

Add '-0.04166666667' to each side of the equation.
0.04166666667 + 5.041666667x + -0.04166666667 + x2 = 0 + -0.04166666667

Reorder the terms:
0.04166666667 + -0.04166666667 + 5.041666667x + x2 = 0 + -0.04166666667

Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000
0.00000000000 + 5.041666667x + x2 = 0 + -0.04166666667
5.041666667x + x2 = 0 + -0.04166666667

Combine like terms: 0 + -0.04166666667 = -0.04166666667
5.041666667x + x2 = -0.04166666667

The x term is 5.041666667x.  Take half its coefficient (2.520833334).
Square it (6.354600698) and add it to both sides.

Add '6.354600698' to each side of the equation.
5.041666667x + 6.354600698 + x2 = -0.04166666667 + 6.354600698

Reorder the terms:
6.354600698 + 5.041666667x + x2 = -0.04166666667 + 6.354600698

Combine like terms: -0.04166666667 + 6.354600698 = 6.31293403133
6.354600698 + 5.041666667x + x2 = 6.31293403133

Factor a perfect square on the left side:
(x + 2.520833334)(x + 2.520833334) = 6.31293403133

Calculate the square root of the right side: 2.512555279

Break this problem into two subproblems by setting 
(x + 2.520833334) equal to 2.512555279 and -2.512555279.

Subproblem 1
x + 2.520833334 = 2.512555279

Simplifying
x + 2.520833334 = 2.512555279

Reorder the terms:
2.520833334 + x = 2.512555279

Solving
2.520833334 + x = 2.512555279

Solving for variable 'x'.

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

Add '-2.520833334' to each side of the equation.
2.520833334 + -2.520833334 + x = 2.512555279 + -2.520833334

Combine like terms: 2.520833334 + -2.520833334 = 0.000000000
0.000000000 + x = 2.512555279 + -2.520833334
x = 2.512555279 + -2.520833334

Combine like terms: 2.512555279 + -2.520833334 = -0.008278055
x = -0.008278055

Simplifying
x = -0.008278055

Subproblem 2
x + 2.520833334 = -2.512555279

Simplifying
x + 2.520833334 = -2.512555279

Reorder the terms:
2.520833334 + x = -2.512555279

Solving
2.520833334 + x = -2.512555279

Solving for variable 'x'.

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

Add '-2.520833334' to each side of the equation.
2.520833334 + -2.520833334 + x = -2.512555279 + -2.520833334

Combine like terms: 2.520833334 + -2.520833334 = 0.000000000
0.000000000 + x = -2.512555279 + -2.520833334
x = -2.512555279 + -2.520833334

Combine like terms: -2.512555279 + -2.520833334 = -5.033388613
x = -5.033388613

Simplifying
x = -5.033388613

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.008278055, -5.033388613}
Solution
x = {-0.008278055, -5.033388613}