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

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


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

Multiply F * x
xF = x(2x + -1)(x + 1)

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

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

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

Combine like terms: -1x + 2x = 1x
xF = x(-1 + 1x + 2x2)
xF = (-1 * x + 1x * x + 2x2 * x)
xF = (-1x + 1x2 + 2x3)

Solving
xF = -1x + 1x2 + 2x3

Solving for variable 'x'.

Reorder the terms:
x + xF + -1x2 + -2x3 = -1x + 1x2 + 2x3 + x + -1x2 + -2x3

Reorder the terms:
x + xF + -1x2 + -2x3 = -1x + x + 1x2 + -1x2 + 2x3 + -2x3

Combine like terms: -1x + x = 0
x + xF + -1x2 + -2x3 = 0 + 1x2 + -1x2 + 2x3 + -2x3
x + xF + -1x2 + -2x3 = 1x2 + -1x2 + 2x3 + -2x3

Combine like terms: 1x2 + -1x2 = 0
x + xF + -1x2 + -2x3 = 0 + 2x3 + -2x3
x + xF + -1x2 + -2x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
x + xF + -1x2 + -2x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + F + -1x + -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 '(1 + F + -1x + -2x2)' equal to zero and attempt to solve:

Simplifying
1 + F + -1x + -2x2 = 0

Solving
1 + F + -1x + -2x2 = 0

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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