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

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

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

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

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

Multiply -1 * 6
-6x(-6 + x) = -8x + 3(-1x + -6)
(-6 * -6x + x * -6x) = -8x + 3(-1x + -6)
(36x + -6x2) = -8x + 3(-1x + -6)

Reorder the terms:
36x + -6x2 = -8x + 3(-6 + -1x)
36x + -6x2 = -8x + (-6 * 3 + -1x * 3)
36x + -6x2 = -8x + (-18 + -3x)

Reorder the terms:
36x + -6x2 = -18 + -8x + -3x

Combine like terms: -8x + -3x = -11x
36x + -6x2 = -18 + -11x

Solving
36x + -6x2 = -18 + -11x

Solving for variable 'x'.

Reorder the terms:
18 + 36x + 11x + -6x2 = -18 + -11x + 18 + 11x

Combine like terms: 36x + 11x = 47x
18 + 47x + -6x2 = -18 + -11x + 18 + 11x

Reorder the terms:
18 + 47x + -6x2 = -18 + 18 + -11x + 11x

Combine like terms: -18 + 18 = 0
18 + 47x + -6x2 = 0 + -11x + 11x
18 + 47x + -6x2 = -11x + 11x

Combine like terms: -11x + 11x = 0
18 + 47x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-3 + -7.833333333x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -7.833333333x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -7.833333333x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7.833333333x + x2 = 0 + 3
-7.833333333x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-7.833333333x + x2 = 3

The x term is -7.833333333x.  Take half its coefficient (-3.916666667).
Square it (15.34027778) and add it to both sides.

Add '15.34027778' to each side of the equation.
-7.833333333x + 15.34027778 + x2 = 3 + 15.34027778

Reorder the terms:
15.34027778 + -7.833333333x + x2 = 3 + 15.34027778

Combine like terms: 3 + 15.34027778 = 18.34027778
15.34027778 + -7.833333333x + x2 = 18.34027778

Factor a perfect square on the left side:
(x + -3.916666667)(x + -3.916666667) = 18.34027778

Calculate the square root of the right side: 4.282555053

Break this problem into two subproblems by setting 
(x + -3.916666667) equal to 4.282555053 and -4.282555053.

Subproblem 1
x + -3.916666667 = 4.282555053

Simplifying
x + -3.916666667 = 4.282555053

Reorder the terms:
-3.916666667 + x = 4.282555053

Solving
-3.916666667 + x = 4.282555053

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x = 4.282555053 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x = 4.282555053 + 3.916666667
x = 4.282555053 + 3.916666667

Combine like terms: 4.282555053 + 3.916666667 = 8.19922172
x = 8.19922172

Simplifying
x = 8.19922172

Subproblem 2
x + -3.916666667 = -4.282555053

Simplifying
x + -3.916666667 = -4.282555053

Reorder the terms:
-3.916666667 + x = -4.282555053

Solving
-3.916666667 + x = -4.282555053

Solving for variable 'x'.

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

Add '3.916666667' to each side of the equation.
-3.916666667 + 3.916666667 + x = -4.282555053 + 3.916666667

Combine like terms: -3.916666667 + 3.916666667 = 0.000000000
0.000000000 + x = -4.282555053 + 3.916666667
x = -4.282555053 + 3.916666667

Combine like terms: -4.282555053 + 3.916666667 = -0.365888386
x = -0.365888386

Simplifying
x = -0.365888386

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.19922172, -0.365888386}