2(8x-2)-x(5x+7)=6-x(3x+1)

Solution for 2(8x-2)-x(5x+7)=6-x(3x+1) equation:

Simplifying
2(8x + -2) + -1x(5x + 7) = 6 + -1x(3x + 1)

Reorder the terms:
2(-2 + 8x) + -1x(5x + 7) = 6 + -1x(3x + 1)
(-2 * 2 + 8x * 2) + -1x(5x + 7) = 6 + -1x(3x + 1)
(-4 + 16x) + -1x(5x + 7) = 6 + -1x(3x + 1)

Reorder the terms:
-4 + 16x + -1x(7 + 5x) = 6 + -1x(3x + 1)
-4 + 16x + (7 * -1x + 5x * -1x) = 6 + -1x(3x + 1)
-4 + 16x + (-7x + -5x2) = 6 + -1x(3x + 1)

Combine like terms: 16x + -7x = 9x
-4 + 9x + -5x2 = 6 + -1x(3x + 1)

Reorder the terms:
-4 + 9x + -5x2 = 6 + -1x(1 + 3x)
-4 + 9x + -5x2 = 6 + (1 * -1x + 3x * -1x)
-4 + 9x + -5x2 = 6 + (-1x + -3x2)

Solving
-4 + 9x + -5x2 = 6 + -1x + -3x2

Solving for variable 'x'.

Reorder the terms:
-4 + -6 + 9x + x + -5x2 + 3x2 = 6 + -1x + -3x2 + -6 + x + 3x2

Combine like terms: -4 + -6 = -10
-10 + 9x + x + -5x2 + 3x2 = 6 + -1x + -3x2 + -6 + x + 3x2

Combine like terms: 9x + x = 10x
-10 + 10x + -5x2 + 3x2 = 6 + -1x + -3x2 + -6 + x + 3x2

Combine like terms: -5x2 + 3x2 = -2x2
-10 + 10x + -2x2 = 6 + -1x + -3x2 + -6 + x + 3x2

Reorder the terms:
-10 + 10x + -2x2 = 6 + -6 + -1x + x + -3x2 + 3x2

Combine like terms: 6 + -6 = 0
-10 + 10x + -2x2 = 0 + -1x + x + -3x2 + 3x2
-10 + 10x + -2x2 = -1x + x + -3x2 + 3x2

Combine like terms: -1x + x = 0
-10 + 10x + -2x2 = 0 + -3x2 + 3x2
-10 + 10x + -2x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-10 + 10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 5x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 5x + -1x2)' equal to zero and attempt to solve:

Simplifying
-5 + 5x + -1x2 = 0

Solving
-5 + 5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -5x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -5x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -5x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5x + x2 = 0 + -5
-5x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-5x + x2 = -5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + -5x + x2 = 1.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
x + -2.5 = 1.118033989

Simplifying
x + -2.5 = 1.118033989

Reorder the terms:
-2.5 + x = 1.118033989

Solving
-2.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.118033989 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.118033989 + 2.5
x = 1.118033989 + 2.5

Combine like terms: 1.118033989 + 2.5 = 3.618033989
x = 3.618033989

Simplifying
x = 3.618033989

Subproblem 2
x + -2.5 = -1.118033989

Simplifying
x + -2.5 = -1.118033989

Reorder the terms:
-2.5 + x = -1.118033989

Solving
-2.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.118033989 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.118033989 + 2.5
x = -1.118033989 + 2.5

Combine like terms: -1.118033989 + 2.5 = 1.381966011
x = 1.381966011

Simplifying
x = 1.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.618033989, 1.381966011}
Solution
x = {3.618033989, 1.381966011}