F(x)=-x^6+2x^3-x

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Solution for F(x)=-x^6+2x^3-x equation: 


Simplifying
F(x) = -1x6 + 2x3 + -1x

Multiply F * x
xF = -1x6 + 2x3 + -1x

Reorder the terms:
xF = -1x + 2x3 + -1x6

Solving
xF = -1x + 2x3 + -1x6

Solving for variable 'x'.

Reorder the terms:
x + xF + -2x3 + x6 = -1x + 2x3 + -1x6 + x + -2x3 + x6

Reorder the terms:
x + xF + -2x3 + x6 = -1x + x + 2x3 + -2x3 + -1x6 + x6

Combine like terms: -1x + x = 0
x + xF + -2x3 + x6 = 0 + 2x3 + -2x3 + -1x6 + x6
x + xF + -2x3 + x6 = 2x3 + -2x3 + -1x6 + x6

Combine like terms: 2x3 + -2x3 = 0
x + xF + -2x3 + x6 = 0 + -1x6 + x6
x + xF + -2x3 + x6 = -1x6 + x6

Combine like terms: -1x6 + x6 = 0
x + xF + -2x3 + x6 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + F + -2x2 + x5) = 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 + -2x2 + x5)' equal to zero and attempt to solve:

Simplifying
1 + F + -2x2 + x5 = 0

Solving
1 + F + -2x2 + x5 = 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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