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

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


Simplifying
F(x) = 2x4 + 2x3 + -1x2 + -1x

Multiply F * x
xF = 2x4 + 2x3 + -1x2 + -1x

Reorder the terms:
xF = -1x + -1x2 + 2x3 + 2x4

Solving
xF = -1x + -1x2 + 2x3 + 2x4

Solving for variable 'x'.

Reorder the terms:
x + xF + x2 + -2x3 + -2x4 = -1x + -1x2 + 2x3 + 2x4 + x + x2 + -2x3 + -2x4

Reorder the terms:
x + xF + x2 + -2x3 + -2x4 = -1x + x + -1x2 + x2 + 2x3 + -2x3 + 2x4 + -2x4

Combine like terms: -1x + x = 0
x + xF + x2 + -2x3 + -2x4 = 0 + -1x2 + x2 + 2x3 + -2x3 + 2x4 + -2x4
x + xF + x2 + -2x3 + -2x4 = -1x2 + x2 + 2x3 + -2x3 + 2x4 + -2x4

Combine like terms: -1x2 + x2 = 0
x + xF + x2 + -2x3 + -2x4 = 0 + 2x3 + -2x3 + 2x4 + -2x4
x + xF + x2 + -2x3 + -2x4 = 2x3 + -2x3 + 2x4 + -2x4

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + F + x + -2x2 + -2x3) = 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 + x + -2x2 + -2x3)' equal to zero and attempt to solve: Simplifying 1 + F + x + -2x2 + -2x3 = 0 Solving 1 + F + x + -2x2 + -2x3 = 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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