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

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

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

Remove parenthesis around (-2x)
-2 + x * -2x = x + -6

Reorder the terms for easier multiplication:
-2 + -2x * x = x + -6

Multiply x * x
-2 + -2x2 = x + -6

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

Solving
-2 + -2x2 = -6 + x

Solving for variable 'x'.

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

Combine like terms: -2 + 6 = 4
4 + -1x + -2x2 = -6 + x + 6 + -1x

Reorder the terms:
4 + -1x + -2x2 = -6 + 6 + x + -1x

Combine like terms: -6 + 6 = 0
4 + -1x + -2x2 = 0 + x + -1x
4 + -1x + -2x2 = x + -1x

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

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

Divide each side by '-2'.
-2 + 0.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.5x + x2 = 0 + 2
0.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.5x + x2 = 2

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 2 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 2 + 0.0625

Combine like terms: 2 + 0.0625 = 2.0625
0.0625 + 0.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.436140662 and -1.436140662.

Subproblem 1
x + 0.25 = 1.436140662

Simplifying
x + 0.25 = 1.436140662

Reorder the terms:
0.25 + x = 1.436140662

Solving
0.25 + x = 1.436140662

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.436140662 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.436140662 + -0.25
x = 1.436140662 + -0.25

Combine like terms: 1.436140662 + -0.25 = 1.186140662
x = 1.186140662

Simplifying
x = 1.186140662

Subproblem 2
x + 0.25 = -1.436140662

Simplifying
x + 0.25 = -1.436140662

Reorder the terms:
0.25 + x = -1.436140662

Solving
0.25 + x = -1.436140662

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.436140662 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.436140662 + -0.25
x = -1.436140662 + -0.25

Combine like terms: -1.436140662 + -0.25 = -1.686140662
x = -1.686140662

Simplifying
x = -1.686140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.186140662, -1.686140662}