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

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


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

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

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

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

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

Solving for variable 'x'.

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

Reorder the terms:
-2 + -6x + -4x2 = 8x + -8x + 4x2 + -4x2

Combine like terms: 8x + -8x = 0
-2 + -6x + -4x2 = 0 + 4x2 + -4x2
-2 + -6x + -4x2 = 4x2 + -4x2

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

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

Factor a trinomial.
-2((1 + x)(1 + 2x)) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1, -0.5}

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