-8+6(-x-3)4x=x

Solution for -8+6(-x-3)4x=x equation:

Simplifying
-8 + 6(-1x + -3) * 4x = x

Reorder the terms:
-8 + 6(-3 + -1x) * 4x = x

Reorder the terms for easier multiplication:
-8 + 6 * 4x(-3 + -1x) = x

Multiply 6 * 4
-8 + 24x(-3 + -1x) = x
-8 + (-3 * 24x + -1x * 24x) = x
-8 + (-72x + -24x2) = x

Solving
-8 + -72x + -24x2 = x

Solving for variable 'x'.

Reorder the terms:
-8 + -72x + -1x + -24x2 = x + -1x

Combine like terms: -72x + -1x = -73x
-8 + -73x + -24x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + -73x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 73x + 24x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(8 + 73x + 24x2)' equal to zero and attempt to solve:

Simplifying
8 + 73x + 24x2 = 0

Solving
8 + 73x + 24x2 = 0

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

Divide each side by '24'.
0.3333333333 + 3.041666667x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 3.041666667x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 3.041666667x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 3.041666667x + x2 = 0 + -0.3333333333
3.041666667x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
3.041666667x + x2 = -0.3333333333

The x term is 3.041666667x.  Take half its coefficient (1.520833334).
Square it (2.312934030) and add it to both sides.

Add '2.312934030' to each side of the equation.
3.041666667x + 2.312934030 + x2 = -0.3333333333 + 2.312934030

Reorder the terms:
2.312934030 + 3.041666667x + x2 = -0.3333333333 + 2.312934030

Combine like terms: -0.3333333333 + 2.312934030 = 1.9796006967
2.312934030 + 3.041666667x + x2 = 1.9796006967

Factor a perfect square on the left side:
(x + 1.520833334)(x + 1.520833334) = 1.9796006967

Calculate the square root of the right side: 1.406982835

Break this problem into two subproblems by setting 
(x + 1.520833334) equal to 1.406982835 and -1.406982835.

Subproblem 1
x + 1.520833334 = 1.406982835

Simplifying
x + 1.520833334 = 1.406982835

Reorder the terms:
1.520833334 + x = 1.406982835

Solving
1.520833334 + x = 1.406982835

Solving for variable 'x'.

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

Add '-1.520833334' to each side of the equation.
1.520833334 + -1.520833334 + x = 1.406982835 + -1.520833334

Combine like terms: 1.520833334 + -1.520833334 = 0.000000000
0.000000000 + x = 1.406982835 + -1.520833334
x = 1.406982835 + -1.520833334

Combine like terms: 1.406982835 + -1.520833334 = -0.113850499
x = -0.113850499

Simplifying
x = -0.113850499

Subproblem 2
x + 1.520833334 = -1.406982835

Simplifying
x + 1.520833334 = -1.406982835

Reorder the terms:
1.520833334 + x = -1.406982835

Solving
1.520833334 + x = -1.406982835

Solving for variable 'x'.

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

Add '-1.520833334' to each side of the equation.
1.520833334 + -1.520833334 + x = -1.406982835 + -1.520833334

Combine like terms: 1.520833334 + -1.520833334 = 0.000000000
0.000000000 + x = -1.406982835 + -1.520833334
x = -1.406982835 + -1.520833334

Combine like terms: -1.406982835 + -1.520833334 = -2.927816169
x = -2.927816169

Simplifying
x = -2.927816169

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.113850499, -2.927816169}
Solution
x = {-0.113850499, -2.927816169}