G(x)=-2x^3+2x

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Solution for G(x)=-2x^3+2x equation: 


Simplifying
G(x) = -2x3 + 2x

Multiply G * x
xG = -2x3 + 2x

Reorder the terms:
xG = 2x + -2x3

Solving
xG = 2x + -2x3

Solving for variable 'x'.

Reorder the terms:
-2x + xG + 2x3 = 2x + -2x3 + -2x + 2x3

Reorder the terms:
-2x + xG + 2x3 = 2x + -2x + -2x3 + 2x3

Combine like terms: 2x + -2x = 0
-2x + xG + 2x3 = 0 + -2x3 + 2x3
-2x + xG + 2x3 = -2x3 + 2x3

Combine like terms: -2x3 + 2x3 = 0
-2x + xG + 2x3 = 0

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


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 + G + 2x2)' equal to zero and attempt to solve:

Simplifying
-2 + G + 2x2 = 0

Solving
-2 + G + 2x2 = 0

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

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

Reorder the terms:
-2 + 2 + G + 2x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + G + 2x2 = 0 + 2
G + 2x2 = 0 + 2

Combine like terms: 0 + 2 = 2
G + 2x2 = 2

Add '-1G' to each side of the equation.
G + -1G + 2x2 = 2 + -1G

Combine like terms: G + -1G = 0
0 + 2x2 = 2 + -1G
2x2 = 2 + -1G

Divide each side by '2'.
x2 = 1 + -0.5G

Simplifying
x2 = 1 + -0.5G

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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