6x-(x-8)=5x(2x-7)

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

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

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

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

Combine like terms: 6x + -1x = 5x
8 + 5x = 5x(2x + -7)

Reorder the terms:
8 + 5x = 5x(-7 + 2x)
8 + 5x = (-7 * 5x + 2x * 5x)
8 + 5x = (-35x + 10x2)

Solving
8 + 5x = -35x + 10x2

Solving for variable 'x'.

Combine like terms: 5x + 35x = 40x
8 + 40x + -10x2 = -35x + 10x2 + 35x + -10x2

Reorder the terms:
8 + 40x + -10x2 = -35x + 35x + 10x2 + -10x2

Combine like terms: -35x + 35x = 0
8 + 40x + -10x2 = 0 + 10x2 + -10x2
8 + 40x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
8 + 40x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 20x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 20x + -5x2)' equal to zero and attempt to solve:

Simplifying
4 + 20x + -5x2 = 0

Solving
4 + 20x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.8 + -4x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -4x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -4x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -4x + x2 = 0 + 0.8
-4x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-4x + x2 = 0.8

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 0.8 + 4

Reorder the terms:
4 + -4x + x2 = 0.8 + 4

Combine like terms: 0.8 + 4 = 4.8
4 + -4x + x2 = 4.8

Factor a perfect square on the left side:
(x + -2)(x + -2) = 4.8

Calculate the square root of the right side: 2.19089023

Break this problem into two subproblems by setting 
(x + -2) equal to 2.19089023 and -2.19089023.

Subproblem 1
x + -2 = 2.19089023

Simplifying
x + -2 = 2.19089023

Reorder the terms:
-2 + x = 2.19089023

Solving
-2 + x = 2.19089023

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.19089023 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.19089023 + 2
x = 2.19089023 + 2

Combine like terms: 2.19089023 + 2 = 4.19089023
x = 4.19089023

Simplifying
x = 4.19089023

Subproblem 2
x + -2 = -2.19089023

Simplifying
x + -2 = -2.19089023

Reorder the terms:
-2 + x = -2.19089023

Solving
-2 + x = -2.19089023

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.19089023 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.19089023 + 2
x = -2.19089023 + 2

Combine like terms: -2.19089023 + 2 = -0.19089023
x = -0.19089023

Simplifying
x = -0.19089023

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.19089023, -0.19089023}
Solution
x = {4.19089023, -0.19089023}