(2x-2x^2-x)-5x=0

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Solution for (2x-2x^2-x)-5x=0 equation: 


Simplifying
(2x + -2x2 + -1x) + -5x = 0

Reorder the terms:
(2x + -1x + -2x2) + -5x = 0

Combine like terms: 2x + -1x = 1x
(1x + -2x2) + -5x = 0

Remove parenthesis around (1x + -2x2)
1x + -2x2 + -5x = 0

Reorder the terms:
1x + -5x + -2x2 = 0

Combine like terms: 1x + -5x = -4x
-4x + -2x2 = 0

Solving
-4x + -2x2 = 0

Solving for variable 'x'.

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

Ignore the factor -2.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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
Solution
x = {0, -2}

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