(x-8)=(x-1)(x+8)+2(x-1)

Solution for (x-8)=(x-1)(x+8)+2(x-1) equation:

Simplifying
(x + -8) = (x + -1)(x + 8) + 2(x + -1)

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

Remove parenthesis around (-8 + x)
-8 + x = (x + -1)(x + 8) + 2(x + -1)

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

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

Multiply (-1 + x) * (8 + x)
-8 + x = (-1(8 + x) + x(8 + x)) + 2(x + -1)
-8 + x = ((8 * -1 + x * -1) + x(8 + x)) + 2(x + -1)
-8 + x = ((-8 + -1x) + x(8 + x)) + 2(x + -1)
-8 + x = (-8 + -1x + (8 * x + x * x)) + 2(x + -1)
-8 + x = (-8 + -1x + (8x + x2)) + 2(x + -1)

Combine like terms: -1x + 8x = 7x
-8 + x = (-8 + 7x + x2) + 2(x + -1)

Reorder the terms:
-8 + x = -8 + 7x + x2 + 2(-1 + x)
-8 + x = -8 + 7x + x2 + (-1 * 2 + x * 2)
-8 + x = -8 + 7x + x2 + (-2 + 2x)

Reorder the terms:
-8 + x = -8 + -2 + 7x + 2x + x2

Combine like terms: -8 + -2 = -10
-8 + x = -10 + 7x + 2x + x2

Combine like terms: 7x + 2x = 9x
-8 + x = -10 + 9x + x2

Solving
-8 + x = -10 + 9x + x2

Solving for variable 'x'.

Reorder the terms:
-8 + 10 + x + -9x + -1x2 = -10 + 9x + x2 + 10 + -9x + -1x2

Combine like terms: -8 + 10 = 2
2 + x + -9x + -1x2 = -10 + 9x + x2 + 10 + -9x + -1x2

Combine like terms: x + -9x = -8x
2 + -8x + -1x2 = -10 + 9x + x2 + 10 + -9x + -1x2

Reorder the terms:
2 + -8x + -1x2 = -10 + 10 + 9x + -9x + x2 + -1x2

Combine like terms: -10 + 10 = 0
2 + -8x + -1x2 = 0 + 9x + -9x + x2 + -1x2
2 + -8x + -1x2 = 9x + -9x + x2 + -1x2

Combine like terms: 9x + -9x = 0
2 + -8x + -1x2 = 0 + x2 + -1x2
2 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -8x + -1x2 = 0

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

Divide each side by '-1'.
-2 + 8x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 8x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 8x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8x + x2 = 0 + 2
8x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
8x + x2 = 2

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 2 + 16

Reorder the terms:
16 + 8x + x2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + 8x + x2 = 18

Factor a perfect square on the left side:
(x + 4)(x + 4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 4) equal to 4.242640687 and -4.242640687.

Subproblem 1
x + 4 = 4.242640687

Simplifying
x + 4 = 4.242640687

Reorder the terms:
4 + x = 4.242640687

Solving
4 + x = 4.242640687

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.242640687 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.242640687 + -4
x = 4.242640687 + -4

Combine like terms: 4.242640687 + -4 = 0.242640687
x = 0.242640687

Simplifying
x = 0.242640687

Subproblem 2
x + 4 = -4.242640687

Simplifying
x + 4 = -4.242640687

Reorder the terms:
4 + x = -4.242640687

Solving
4 + x = -4.242640687

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.242640687 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.242640687 + -4
x = -4.242640687 + -4

Combine like terms: -4.242640687 + -4 = -8.242640687
x = -8.242640687

Simplifying
x = -8.242640687

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.242640687, -8.242640687}