-x-2(x-4)(x-1)=2(x-2)

Solution for -x-2(x-4)(x-1)=2(x-2) equation:

Simplifying
-1x + -2(x + -4)(x + -1) = 2(x + -2)

Reorder the terms:
-1x + -2(-4 + x)(x + -1) = 2(x + -2)

Reorder the terms:
-1x + -2(-4 + x)(-1 + x) = 2(x + -2)

Multiply (-4 + x) * (-1 + x)
-1x + -2(-4(-1 + x) + x(-1 + x)) = 2(x + -2)
-1x + -2((-1 * -4 + x * -4) + x(-1 + x)) = 2(x + -2)
-1x + -2((4 + -4x) + x(-1 + x)) = 2(x + -2)
-1x + -2(4 + -4x + (-1 * x + x * x)) = 2(x + -2)
-1x + -2(4 + -4x + (-1x + x2)) = 2(x + -2)

Combine like terms: -4x + -1x = -5x
-1x + -2(4 + -5x + x2) = 2(x + -2)
-1x + (4 * -2 + -5x * -2 + x2 * -2) = 2(x + -2)
-1x + (-8 + 10x + -2x2) = 2(x + -2)

Reorder the terms:
-8 + -1x + 10x + -2x2 = 2(x + -2)

Combine like terms: -1x + 10x = 9x
-8 + 9x + -2x2 = 2(x + -2)

Reorder the terms:
-8 + 9x + -2x2 = 2(-2 + x)
-8 + 9x + -2x2 = (-2 * 2 + x * 2)
-8 + 9x + -2x2 = (-4 + 2x)

Solving
-8 + 9x + -2x2 = -4 + 2x

Solving for variable 'x'.

Reorder the terms:
-8 + 4 + 9x + -2x + -2x2 = -4 + 2x + 4 + -2x

Combine like terms: -8 + 4 = -4
-4 + 9x + -2x + -2x2 = -4 + 2x + 4 + -2x

Combine like terms: 9x + -2x = 7x
-4 + 7x + -2x2 = -4 + 2x + 4 + -2x

Reorder the terms:
-4 + 7x + -2x2 = -4 + 4 + 2x + -2x

Combine like terms: -4 + 4 = 0
-4 + 7x + -2x2 = 0 + 2x + -2x
-4 + 7x + -2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-4 + 7x + -2x2 = 0

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

Divide each side by '-2'.
2 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -3.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.5x + x2 = 0 + -2
-3.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.5x + x2 = -2

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -2 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -2 + 3.0625

Combine like terms: -2 + 3.0625 = 1.0625
3.0625 + -3.5x + x2 = 1.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.030776406 and -1.030776406.

Subproblem 1
x + -1.75 = 1.030776406

Simplifying
x + -1.75 = 1.030776406

Reorder the terms:
-1.75 + x = 1.030776406

Solving
-1.75 + x = 1.030776406

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 1.030776406 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 1.030776406 + 1.75
x = 1.030776406 + 1.75

Combine like terms: 1.030776406 + 1.75 = 2.780776406
x = 2.780776406

Simplifying
x = 2.780776406

Subproblem 2
x + -1.75 = -1.030776406

Simplifying
x + -1.75 = -1.030776406

Reorder the terms:
-1.75 + x = -1.030776406

Solving
-1.75 + x = -1.030776406

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -1.030776406 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -1.030776406 + 1.75
x = -1.030776406 + 1.75

Combine like terms: -1.030776406 + 1.75 = 0.719223594
x = 0.719223594

Simplifying
x = 0.719223594

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.780776406, 0.719223594}