(x-5)(x-2)-(9x-9)(x-6)=

Solution for (x-5)(x-2)-(9x-9)(x-6)= equation:

Simplifying
(x + -5)(x + -2) + -1(9x + -9)(x + -6) = 0

Reorder the terms:
(-5 + x)(x + -2) + -1(9x + -9)(x + -6) = 0

Reorder the terms:
(-5 + x)(-2 + x) + -1(9x + -9)(x + -6) = 0

Multiply (-5 + x) * (-2 + x)
(-5(-2 + x) + x(-2 + x)) + -1(9x + -9)(x + -6) = 0
((-2 * -5 + x * -5) + x(-2 + x)) + -1(9x + -9)(x + -6) = 0
((10 + -5x) + x(-2 + x)) + -1(9x + -9)(x + -6) = 0
(10 + -5x + (-2 * x + x * x)) + -1(9x + -9)(x + -6) = 0
(10 + -5x + (-2x + x2)) + -1(9x + -9)(x + -6) = 0

Combine like terms: -5x + -2x = -7x
(10 + -7x + x2) + -1(9x + -9)(x + -6) = 0

Reorder the terms:
10 + -7x + x2 + -1(-9 + 9x)(x + -6) = 0

Reorder the terms:
10 + -7x + x2 + -1(-9 + 9x)(-6 + x) = 0

Multiply (-9 + 9x) * (-6 + x)
10 + -7x + x2 + -1(-9(-6 + x) + 9x * (-6 + x)) = 0
10 + -7x + x2 + -1((-6 * -9 + x * -9) + 9x * (-6 + x)) = 0
10 + -7x + x2 + -1((54 + -9x) + 9x * (-6 + x)) = 0
10 + -7x + x2 + -1(54 + -9x + (-6 * 9x + x * 9x)) = 0
10 + -7x + x2 + -1(54 + -9x + (-54x + 9x2)) = 0

Combine like terms: -9x + -54x = -63x
10 + -7x + x2 + -1(54 + -63x + 9x2) = 0
10 + -7x + x2 + (54 * -1 + -63x * -1 + 9x2 * -1) = 0
10 + -7x + x2 + (-54 + 63x + -9x2) = 0

Reorder the terms:
10 + -54 + -7x + 63x + x2 + -9x2 = 0

Combine like terms: 10 + -54 = -44
-44 + -7x + 63x + x2 + -9x2 = 0

Combine like terms: -7x + 63x = 56x
-44 + 56x + x2 + -9x2 = 0

Combine like terms: x2 + -9x2 = -8x2
-44 + 56x + -8x2 = 0

Solving
-44 + 56x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-11 + 14x + -2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-11 + 14x + -2x2)' equal to zero and attempt to solve:

Simplifying
-11 + 14x + -2x2 = 0

Solving
-11 + 14x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
5.5 + -7x + x2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -7x + -5.5 + x2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -7x + x2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -7x + x2 = 0 + -5.5
-7x + x2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-7x + x2 = -5.5

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -5.5 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -5.5 + 12.25

Combine like terms: -5.5 + 12.25 = 6.75
12.25 + -7x + x2 = 6.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(x + -3.5) equal to 2.598076211 and -2.598076211.

Subproblem 1
x + -3.5 = 2.598076211

Simplifying
x + -3.5 = 2.598076211

Reorder the terms:
-3.5 + x = 2.598076211

Solving
-3.5 + x = 2.598076211

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 2.598076211 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 2.598076211 + 3.5
x = 2.598076211 + 3.5

Combine like terms: 2.598076211 + 3.5 = 6.098076211
x = 6.098076211

Simplifying
x = 6.098076211

Subproblem 2
x + -3.5 = -2.598076211

Simplifying
x + -3.5 = -2.598076211

Reorder the terms:
-3.5 + x = -2.598076211

Solving
-3.5 + x = -2.598076211

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -2.598076211 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -2.598076211 + 3.5
x = -2.598076211 + 3.5

Combine like terms: -2.598076211 + 3.5 = 0.901923789
x = 0.901923789

Simplifying
x = 0.901923789

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.098076211, 0.901923789}
Solution
x = {6.098076211, 0.901923789}