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

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


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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

Solving
2 + F + x + -1x2 = 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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