2x+10-9x=-(x+8)(x-2)+(x-2)

Solution for 2x+10-9x=-(x+8)(x-2)+(x-2) equation:

Simplifying
2x + 10 + -9x = -1(x + 8)(x + -2) + (x + -2)

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

Combine like terms: 2x + -9x = -7x
10 + -7x = -1(x + 8)(x + -2) + (x + -2)

Reorder the terms:
10 + -7x = -1(8 + x)(x + -2) + (x + -2)

Reorder the terms:
10 + -7x = -1(8 + x)(-2 + x) + (x + -2)

Multiply (8 + x) * (-2 + x)
10 + -7x = -1(8(-2 + x) + x(-2 + x)) + (x + -2)
10 + -7x = -1((-2 * 8 + x * 8) + x(-2 + x)) + (x + -2)
10 + -7x = -1((-16 + 8x) + x(-2 + x)) + (x + -2)
10 + -7x = -1(-16 + 8x + (-2 * x + x * x)) + (x + -2)
10 + -7x = -1(-16 + 8x + (-2x + x2)) + (x + -2)

Combine like terms: 8x + -2x = 6x
10 + -7x = -1(-16 + 6x + x2) + (x + -2)
10 + -7x = (-16 * -1 + 6x * -1 + x2 * -1) + (x + -2)
10 + -7x = (16 + -6x + -1x2) + (x + -2)

Reorder the terms:
10 + -7x = 16 + -6x + -1x2 + (-2 + x)

Remove parenthesis around (-2 + x)
10 + -7x = 16 + -6x + -1x2 + -2 + x

Reorder the terms:
10 + -7x = 16 + -2 + -6x + x + -1x2

Combine like terms: 16 + -2 = 14
10 + -7x = 14 + -6x + x + -1x2

Combine like terms: -6x + x = -5x
10 + -7x = 14 + -5x + -1x2

Solving
10 + -7x = 14 + -5x + -1x2

Solving for variable 'x'.

Reorder the terms:
10 + -14 + -7x + 5x + x2 = 14 + -5x + -1x2 + -14 + 5x + x2

Combine like terms: 10 + -14 = -4
-4 + -7x + 5x + x2 = 14 + -5x + -1x2 + -14 + 5x + x2

Combine like terms: -7x + 5x = -2x
-4 + -2x + x2 = 14 + -5x + -1x2 + -14 + 5x + x2

Reorder the terms:
-4 + -2x + x2 = 14 + -14 + -5x + 5x + -1x2 + x2

Combine like terms: 14 + -14 = 0
-4 + -2x + x2 = 0 + -5x + 5x + -1x2 + x2
-4 + -2x + x2 = -5x + 5x + -1x2 + x2

Combine like terms: -5x + 5x = 0
-4 + -2x + x2 = 0 + -1x2 + x2
-4 + -2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-4 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -2x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2x + x2 = 0 + 4
-2x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2x + x2 = 4

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 4 + 1

Reorder the terms:
1 + -2x + x2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2x + x2 = 5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
x + -1 = 2.236067978

Simplifying
x + -1 = 2.236067978

Reorder the terms:
-1 + x = 2.236067978

Solving
-1 + x = 2.236067978

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.236067978 + 1
x = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
x = 3.236067978

Simplifying
x = 3.236067978

Subproblem 2
x + -1 = -2.236067978

Simplifying
x + -1 = -2.236067978

Reorder the terms:
-1 + x = -2.236067978

Solving
-1 + x = -2.236067978

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.236067978 + 1
x = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
x = -1.236067978

Simplifying
x = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.236067978, -1.236067978}