4(3x-5)=-2x(-x+8)-6x

Solution for 4(3x-5)=-2x(-x+8)-6x equation:

Simplifying
4(3x + -5) = -2x(-1x + 8) + -6x

Reorder the terms:
4(-5 + 3x) = -2x(-1x + 8) + -6x
(-5 * 4 + 3x * 4) = -2x(-1x + 8) + -6x
(-20 + 12x) = -2x(-1x + 8) + -6x

Reorder the terms:
-20 + 12x = -2x(8 + -1x) + -6x
-20 + 12x = (8 * -2x + -1x * -2x) + -6x
-20 + 12x = (-16x + 2x2) + -6x

Reorder the terms:
-20 + 12x = -16x + -6x + 2x2

Combine like terms: -16x + -6x = -22x
-20 + 12x = -22x + 2x2

Solving
-20 + 12x = -22x + 2x2

Solving for variable 'x'.

Combine like terms: 12x + 22x = 34x
-20 + 34x + -2x2 = -22x + 2x2 + 22x + -2x2

Reorder the terms:
-20 + 34x + -2x2 = -22x + 22x + 2x2 + -2x2

Combine like terms: -22x + 22x = 0
-20 + 34x + -2x2 = 0 + 2x2 + -2x2
-20 + 34x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-20 + 34x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 17x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + 17x + -1x2)' equal to zero and attempt to solve:

Simplifying
-10 + 17x + -1x2 = 0

Solving
-10 + 17x + -1x2 = 0

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

Divide each side by '-1'.
10 + -17x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -17x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -17x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -17x + x2 = 0 + -10
-17x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-17x + x2 = -10

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -10 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -10 + 72.25

Combine like terms: -10 + 72.25 = 62.25
72.25 + -17x + x2 = 62.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + -8.5) equal to 7.889866919 and -7.889866919.

Subproblem 1
x + -8.5 = 7.889866919

Simplifying
x + -8.5 = 7.889866919

Reorder the terms:
-8.5 + x = 7.889866919

Solving
-8.5 + x = 7.889866919

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = 7.889866919 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 7.889866919 + 8.5
x = 7.889866919 + 8.5

Combine like terms: 7.889866919 + 8.5 = 16.389866919
x = 16.389866919

Simplifying
x = 16.389866919

Subproblem 2
x + -8.5 = -7.889866919

Simplifying
x + -8.5 = -7.889866919

Reorder the terms:
-8.5 + x = -7.889866919

Solving
-8.5 + x = -7.889866919

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = -7.889866919 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -7.889866919 + 8.5
x = -7.889866919 + 8.5

Combine like terms: -7.889866919 + 8.5 = 0.610133081
x = 0.610133081

Simplifying
x = 0.610133081

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.389866919, 0.610133081}
Solution
x = {16.389866919, 0.610133081}