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

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

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

Multiply G * x
xG = 2x(x + -1)(x + 1)

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

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

Multiply (-1 + x) * (1 + x)
xG = 2x(-1(1 + x) + x(1 + x))
xG = 2x((1 * -1 + x * -1) + x(1 + x))
xG = 2x((-1 + -1x) + x(1 + x))
xG = 2x(-1 + -1x + (1 * x + x * x))
xG = 2x(-1 + -1x + (1x + x2))

Combine like terms: -1x + 1x = 0
xG = 2x(-1 + 0 + x2)
xG = 2x(-1 + x2)
xG = (-1 * 2x + x2 * 2x)
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}