F(x)=3x^4-10x^3-5x^2+2x

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Solution for F(x)=3x^4-10x^3-5x^2+2x equation: 


Simplifying
F(x) = 3x4 + -10x3 + -5x2 + 2x

Multiply F * x
xF = 3x4 + -10x3 + -5x2 + 2x

Reorder the terms:
xF = 2x + -5x2 + -10x3 + 3x4

Solving
xF = 2x + -5x2 + -10x3 + 3x4

Solving for variable 'x'.

Reorder the terms:
-2x + xF + 5x2 + 10x3 + -3x4 = 2x + -5x2 + -10x3 + 3x4 + -2x + 5x2 + 10x3 + -3x4

Reorder the terms:
-2x + xF + 5x2 + 10x3 + -3x4 = 2x + -2x + -5x2 + 5x2 + -10x3 + 10x3 + 3x4 + -3x4

Combine like terms: 2x + -2x = 0
-2x + xF + 5x2 + 10x3 + -3x4 = 0 + -5x2 + 5x2 + -10x3 + 10x3 + 3x4 + -3x4
-2x + xF + 5x2 + 10x3 + -3x4 = -5x2 + 5x2 + -10x3 + 10x3 + 3x4 + -3x4

Combine like terms: -5x2 + 5x2 = 0
-2x + xF + 5x2 + 10x3 + -3x4 = 0 + -10x3 + 10x3 + 3x4 + -3x4
-2x + xF + 5x2 + 10x3 + -3x4 = -10x3 + 10x3 + 3x4 + -3x4

Combine like terms: -10x3 + 10x3 = 0
-2x + xF + 5x2 + 10x3 + -3x4 = 0 + 3x4 + -3x4
-2x + xF + 5x2 + 10x3 + -3x4 = 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
-2x + xF + 5x2 + 10x3 + -3x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + F + 5x + 10x2 + -3x3) = 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 + 5x + 10x2 + -3x3)' equal to zero and attempt to solve:

Simplifying
-2 + F + 5x + 10x2 + -3x3 = 0

Solving
-2 + F + 5x + 10x2 + -3x3 = 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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