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

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

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

Reorder the terms:
-8x(4 + 3x) + 6x = 4(x + -8) + 4x
(4 * -8x + 3x * -8x) + 6x = 4(x + -8) + 4x
(-32x + -24x2) + 6x = 4(x + -8) + 4x

Reorder the terms:
-32x + 6x + -24x2 = 4(x + -8) + 4x

Combine like terms: -32x + 6x = -26x
-26x + -24x2 = 4(x + -8) + 4x

Reorder the terms:
-26x + -24x2 = 4(-8 + x) + 4x
-26x + -24x2 = (-8 * 4 + x * 4) + 4x
-26x + -24x2 = (-32 + 4x) + 4x

Combine like terms: 4x + 4x = 8x
-26x + -24x2 = -32 + 8x

Solving
-26x + -24x2 = -32 + 8x

Solving for variable 'x'.

Reorder the terms:
32 + -26x + -8x + -24x2 = -32 + 8x + 32 + -8x

Combine like terms: -26x + -8x = -34x
32 + -34x + -24x2 = -32 + 8x + 32 + -8x

Reorder the terms:
32 + -34x + -24x2 = -32 + 32 + 8x + -8x

Combine like terms: -32 + 32 = 0
32 + -34x + -24x2 = 0 + 8x + -8x
32 + -34x + -24x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
32 + -34x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -17x + -12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + -17x + -12x2)' equal to zero and attempt to solve:

Simplifying
16 + -17x + -12x2 = 0

Solving
16 + -17x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-1.333333333 + 1.416666667x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 1.416666667x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 1.416666667x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 1.416666667x + x2 = 0 + 1.333333333
1.416666667x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
1.416666667x + x2 = 1.333333333

The x term is 1.416666667x.  Take half its coefficient (0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
1.416666667x + 0.5017361113 + x2 = 1.333333333 + 0.5017361113

Reorder the terms:
0.5017361113 + 1.416666667x + x2 = 1.333333333 + 0.5017361113

Combine like terms: 1.333333333 + 0.5017361113 = 1.8350694443
0.5017361113 + 1.416666667x + x2 = 1.8350694443

Factor a perfect square on the left side:
(x + 0.7083333335)(x + 0.7083333335) = 1.8350694443

Calculate the square root of the right side: 1.354647351

Break this problem into two subproblems by setting 
(x + 0.7083333335) equal to 1.354647351 and -1.354647351.

Subproblem 1
x + 0.7083333335 = 1.354647351

Simplifying
x + 0.7083333335 = 1.354647351

Reorder the terms:
0.7083333335 + x = 1.354647351

Solving
0.7083333335 + x = 1.354647351

Solving for variable 'x'.

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

Add '-0.7083333335' to each side of the equation.
0.7083333335 + -0.7083333335 + x = 1.354647351 + -0.7083333335

Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000
0.0000000000 + x = 1.354647351 + -0.7083333335
x = 1.354647351 + -0.7083333335

Combine like terms: 1.354647351 + -0.7083333335 = 0.6463140175
x = 0.6463140175

Simplifying
x = 0.6463140175

Subproblem 2
x + 0.7083333335 = -1.354647351

Simplifying
x + 0.7083333335 = -1.354647351

Reorder the terms:
0.7083333335 + x = -1.354647351

Solving
0.7083333335 + x = -1.354647351

Solving for variable 'x'.

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

Add '-0.7083333335' to each side of the equation.
0.7083333335 + -0.7083333335 + x = -1.354647351 + -0.7083333335

Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000
0.0000000000 + x = -1.354647351 + -0.7083333335
x = -1.354647351 + -0.7083333335

Combine like terms: -1.354647351 + -0.7083333335 = -2.0629806845
x = -2.0629806845

Simplifying
x = -2.0629806845

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6463140175, -2.0629806845}
Solution
x = {0.6463140175, -2.0629806845}