-(6x+4)+40(x-6)(4x-4)=6

Solution for -(6x+4)+40(x-6)(4x-4)=6 equation:

Simplifying
-1(6x + 4) + 40(x + -6)(4x + -4) = 6

Reorder the terms:
-1(4 + 6x) + 40(x + -6)(4x + -4) = 6
(4 * -1 + 6x * -1) + 40(x + -6)(4x + -4) = 6
(-4 + -6x) + 40(x + -6)(4x + -4) = 6

Reorder the terms:
-4 + -6x + 40(-6 + x)(4x + -4) = 6

Reorder the terms:
-4 + -6x + 40(-6 + x)(-4 + 4x) = 6

Multiply (-6 + x) * (-4 + 4x)
-4 + -6x + 40(-6(-4 + 4x) + x(-4 + 4x)) = 6
-4 + -6x + 40((-4 * -6 + 4x * -6) + x(-4 + 4x)) = 6
-4 + -6x + 40((24 + -24x) + x(-4 + 4x)) = 6
-4 + -6x + 40(24 + -24x + (-4 * x + 4x * x)) = 6
-4 + -6x + 40(24 + -24x + (-4x + 4x2)) = 6

Combine like terms: -24x + -4x = -28x
-4 + -6x + 40(24 + -28x + 4x2) = 6
-4 + -6x + (24 * 40 + -28x * 40 + 4x2 * 40) = 6
-4 + -6x + (960 + -1120x + 160x2) = 6

Reorder the terms:
-4 + 960 + -6x + -1120x + 160x2 = 6

Combine like terms: -4 + 960 = 956
956 + -6x + -1120x + 160x2 = 6

Combine like terms: -6x + -1120x = -1126x
956 + -1126x + 160x2 = 6

Solving
956 + -1126x + 160x2 = 6

Solving for variable 'x'.

Reorder the terms:
956 + -6 + -1126x + 160x2 = 6 + -6

Combine like terms: 956 + -6 = 950
950 + -1126x + 160x2 = 6 + -6

Combine like terms: 6 + -6 = 0
950 + -1126x + 160x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(475 + -563x + 80x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(475 + -563x + 80x2)' equal to zero and attempt to solve:

Simplifying
475 + -563x + 80x2 = 0

Solving
475 + -563x + 80x2 = 0

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

Divide each side by '80'.
5.9375 + -7.0375x + x2 = 0.0

Move the constant term to the right:

Add '-5.9375' to each side of the equation.
5.9375 + -7.0375x + -5.9375 + x2 = 0.0 + -5.9375

Reorder the terms:
5.9375 + -5.9375 + -7.0375x + x2 = 0.0 + -5.9375

Combine like terms: 5.9375 + -5.9375 = 0.0000
0.0000 + -7.0375x + x2 = 0.0 + -5.9375
-7.0375x + x2 = 0.0 + -5.9375

Combine like terms: 0.0 + -5.9375 = -5.9375
-7.0375x + x2 = -5.9375

The x term is -7.0375x.  Take half its coefficient (-3.51875).
Square it (12.38160156) and add it to both sides.

Add '12.38160156' to each side of the equation.
-7.0375x + 12.38160156 + x2 = -5.9375 + 12.38160156

Reorder the terms:
12.38160156 + -7.0375x + x2 = -5.9375 + 12.38160156

Combine like terms: -5.9375 + 12.38160156 = 6.44410156
12.38160156 + -7.0375x + x2 = 6.44410156

Factor a perfect square on the left side:
(x + -3.51875)(x + -3.51875) = 6.44410156

Calculate the square root of the right side: 2.5385235

Break this problem into two subproblems by setting 
(x + -3.51875) equal to 2.5385235 and -2.5385235.

Subproblem 1
x + -3.51875 = 2.5385235

Simplifying
x + -3.51875 = 2.5385235

Reorder the terms:
-3.51875 + x = 2.5385235

Solving
-3.51875 + x = 2.5385235

Solving for variable 'x'.

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

Add '3.51875' to each side of the equation.
-3.51875 + 3.51875 + x = 2.5385235 + 3.51875

Combine like terms: -3.51875 + 3.51875 = 0.00000
0.00000 + x = 2.5385235 + 3.51875
x = 2.5385235 + 3.51875

Combine like terms: 2.5385235 + 3.51875 = 6.0572735
x = 6.0572735

Simplifying
x = 6.0572735

Subproblem 2
x + -3.51875 = -2.5385235

Simplifying
x + -3.51875 = -2.5385235

Reorder the terms:
-3.51875 + x = -2.5385235

Solving
-3.51875 + x = -2.5385235

Solving for variable 'x'.

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

Add '3.51875' to each side of the equation.
-3.51875 + 3.51875 + x = -2.5385235 + 3.51875

Combine like terms: -3.51875 + 3.51875 = 0.00000
0.00000 + x = -2.5385235 + 3.51875
x = -2.5385235 + 3.51875

Combine like terms: -2.5385235 + 3.51875 = 0.9802265
x = 0.9802265

Simplifying
x = 0.9802265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.0572735, 0.9802265}
Solution
x = {6.0572735, 0.9802265}