4((x^2-x)-2)+2=4x-2(2-(x^2-x))

Solution for 4((x^2-x)-2)+2=4x-2(2-(x^2-x)) equation:

Simplifying
4((x2 + -1x) + -2) + 2 = 4x + -2(2 + -1(x2 + -1x))

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

Remove parenthesis around (-1x + x2)
4(-1x + x2 + -2) + 2 = 4x + -2(2 + -1(x2 + -1x))

Reorder the terms:
4(-2 + -1x + x2) + 2 = 4x + -2(2 + -1(x2 + -1x))
(-2 * 4 + -1x * 4 + x2 * 4) + 2 = 4x + -2(2 + -1(x2 + -1x))
(-8 + -4x + 4x2) + 2 = 4x + -2(2 + -1(x2 + -1x))

Reorder the terms:
-8 + 2 + -4x + 4x2 = 4x + -2(2 + -1(x2 + -1x))

Combine like terms: -8 + 2 = -6
-6 + -4x + 4x2 = 4x + -2(2 + -1(x2 + -1x))

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

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

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

Solving
-6 + -4x + 4x2 = -4 + 2x + 2x2

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -3x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + -3x + x2 = 0

Solving
-1 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3x + x2 = 0 + 1

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

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

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 = 1 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3x + x2 = 3.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -1.5 = 1.802775638

Simplifying
x + -1.5 = 1.802775638

Reorder the terms:
-1.5 + x = 1.802775638

Solving
-1.5 + x = 1.802775638

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 = 1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.802775638 + 1.5
x = 1.802775638 + 1.5

Combine like terms: 1.802775638 + 1.5 = 3.302775638
x = 3.302775638

Simplifying
x = 3.302775638

Subproblem 2
x + -1.5 = -1.802775638

Simplifying
x + -1.5 = -1.802775638

Reorder the terms:
-1.5 + x = -1.802775638

Solving
-1.5 + x = -1.802775638

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 = -1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.802775638 + 1.5
x = -1.802775638 + 1.5

Combine like terms: -1.802775638 + 1.5 = -0.302775638
x = -0.302775638

Simplifying
x = -0.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.302775638, -0.302775638}
Solution
x = {3.302775638, -0.302775638}