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

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


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

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

Combine like terms: -1x + -2x = -3x
-2 + -3x = 2x(x + 1)

Reorder the terms:
-2 + -3x = 2x(1 + x)
-2 + -3x = (1 * 2x + x * 2x)
-2 + -3x = (2x + 2x2)

Solving
-2 + -3x = 2x + 2x2

Solving for variable 'x'.

Combine like terms: -3x + -2x = -5x
-2 + -5x + -2x2 = 2x + 2x2 + -2x + -2x2

Reorder the terms:
-2 + -5x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
-2 + -5x + -2x2 = 0 + 2x2 + -2x2
-2 + -5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-2 + -5x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 5x + 2x2) = 0

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

Ignore the factor -1.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2

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 = {-2, -0.5}

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