8*-9(x-1)-8(x-2)=(x-2)(x-1)

Solution for 8*-9(x-1)-8(x-2)=(x-2)(x-1) equation:

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

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

Multiply 8 * -9
-72(-1 + x) + -8(x + -2) = (x + -2)(x + -1)
(-1 * -72 + x * -72) + -8(x + -2) = (x + -2)(x + -1)
(72 + -72x) + -8(x + -2) = (x + -2)(x + -1)

Reorder the terms:
72 + -72x + -8(-2 + x) = (x + -2)(x + -1)
72 + -72x + (-2 * -8 + x * -8) = (x + -2)(x + -1)
72 + -72x + (16 + -8x) = (x + -2)(x + -1)

Reorder the terms:
72 + 16 + -72x + -8x = (x + -2)(x + -1)

Combine like terms: 72 + 16 = 88
88 + -72x + -8x = (x + -2)(x + -1)

Combine like terms: -72x + -8x = -80x
88 + -80x = (x + -2)(x + -1)

Reorder the terms:
88 + -80x = (-2 + x)(x + -1)

Reorder the terms:
88 + -80x = (-2 + x)(-1 + x)

Multiply (-2 + x) * (-1 + x)
88 + -80x = (-2(-1 + x) + x(-1 + x))
88 + -80x = ((-1 * -2 + x * -2) + x(-1 + x))
88 + -80x = ((2 + -2x) + x(-1 + x))
88 + -80x = (2 + -2x + (-1 * x + x * x))
88 + -80x = (2 + -2x + (-1x + x2))

Combine like terms: -2x + -1x = -3x
88 + -80x = (2 + -3x + x2)

Solving
88 + -80x = 2 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
88 + -2 + -80x + 3x + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: 88 + -2 = 86
86 + -80x + 3x + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: -80x + 3x = -77x
86 + -77x + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Reorder the terms:
86 + -77x + -1x2 = 2 + -2 + -3x + 3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
86 + -77x + -1x2 = 0 + -3x + 3x + x2 + -1x2
86 + -77x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
86 + -77x + -1x2 = 0 + x2 + -1x2
86 + -77x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
86 + -77x + -1x2 = 0

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

Divide each side by '-1'.
-86 + 77x + x2 = 0

Move the constant term to the right:

Add '86' to each side of the equation.
-86 + 77x + 86 + x2 = 0 + 86

Reorder the terms:
-86 + 86 + 77x + x2 = 0 + 86

Combine like terms: -86 + 86 = 0
0 + 77x + x2 = 0 + 86
77x + x2 = 0 + 86

Combine like terms: 0 + 86 = 86
77x + x2 = 86

The x term is 77x.  Take half its coefficient (38.5).
Square it (1482.25) and add it to both sides.

Add '1482.25' to each side of the equation.
77x + 1482.25 + x2 = 86 + 1482.25

Reorder the terms:
1482.25 + 77x + x2 = 86 + 1482.25

Combine like terms: 86 + 1482.25 = 1568.25
1482.25 + 77x + x2 = 1568.25

Factor a perfect square on the left side:
(x + 38.5)(x + 38.5) = 1568.25

Calculate the square root of the right side: 39.601136347

Break this problem into two subproblems by setting 
(x + 38.5) equal to 39.601136347 and -39.601136347.

Subproblem 1
x + 38.5 = 39.601136347

Simplifying
x + 38.5 = 39.601136347

Reorder the terms:
38.5 + x = 39.601136347

Solving
38.5 + x = 39.601136347

Solving for variable 'x'.

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

Add '-38.5' to each side of the equation.
38.5 + -38.5 + x = 39.601136347 + -38.5

Combine like terms: 38.5 + -38.5 = 0.0
0.0 + x = 39.601136347 + -38.5
x = 39.601136347 + -38.5

Combine like terms: 39.601136347 + -38.5 = 1.101136347
x = 1.101136347

Simplifying
x = 1.101136347

Subproblem 2
x + 38.5 = -39.601136347

Simplifying
x + 38.5 = -39.601136347

Reorder the terms:
38.5 + x = -39.601136347

Solving
38.5 + x = -39.601136347

Solving for variable 'x'.

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

Add '-38.5' to each side of the equation.
38.5 + -38.5 + x = -39.601136347 + -38.5

Combine like terms: 38.5 + -38.5 = 0.0
0.0 + x = -39.601136347 + -38.5
x = -39.601136347 + -38.5

Combine like terms: -39.601136347 + -38.5 = -78.101136347
x = -78.101136347

Simplifying
x = -78.101136347

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.101136347, -78.101136347}