0=x(x-2)-(x+6)

Solution for 0=x(x-2)-(x+6) equation:

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

Reorder the terms:
0 = x(-2 + x) + -1(x + 6)
0 = (-2 * x + x * x) + -1(x + 6)
0 = (-2x + x2) + -1(x + 6)

Reorder the terms:
0 = -2x + x2 + -1(6 + x)
0 = -2x + x2 + (6 * -1 + x * -1)
0 = -2x + x2 + (-6 + -1x)

Reorder the terms:
0 = -6 + -2x + -1x + x2

Combine like terms: -2x + -1x = -3x
0 = -6 + -3x + x2

Solving
0 = -6 + -3x + x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + 3x + -1x2 = -6 + -3x + x2 + 6 + 3x + -1x2

Reorder the terms:
6 + 3x + -1x2 = -6 + 6 + -3x + 3x + x2 + -1x2

Combine like terms: -6 + 6 = 0
6 + 3x + -1x2 = 0 + -3x + 3x + x2 + -1x2
6 + 3x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
6 + 3x + -1x2 = 0 + x2 + -1x2
6 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + 3x + -1x2 = 0

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

Divide each side by '-1'.
-6 + -3x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -3x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -3x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -3x + x2 = 0 + 6
-3x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-3x + x2 = 6

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 6 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + -3x + x2 = 8.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
x + -1.5 = 2.872281323

Simplifying
x + -1.5 = 2.872281323

Reorder the terms:
-1.5 + x = 2.872281323

Solving
-1.5 + x = 2.872281323

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.872281323 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.872281323 + 1.5
x = 2.872281323 + 1.5

Combine like terms: 2.872281323 + 1.5 = 4.372281323
x = 4.372281323

Simplifying
x = 4.372281323

Subproblem 2
x + -1.5 = -2.872281323

Simplifying
x + -1.5 = -2.872281323

Reorder the terms:
-1.5 + x = -2.872281323

Solving
-1.5 + x = -2.872281323

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.872281323 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.872281323 + 1.5
x = -2.872281323 + 1.5

Combine like terms: -2.872281323 + 1.5 = -1.372281323
x = -1.372281323

Simplifying
x = -1.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.372281323, -1.372281323}