0.5x^4-0.5x^2=x^3-x

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Solution for 0.5x^4-0.5x^2=x^3-x equation: 


Simplifying
0.5x4 + -0.5x2 = x3 + -1x

Reorder the terms:
-0.5x2 + 0.5x4 = x3 + -1x

Reorder the terms:
-0.5x2 + 0.5x4 = -1x + x3

Solving
-0.5x2 + 0.5x4 = -1x + x3

Solving for variable 'x'.

Reorder the terms:
x + -0.5x2 + -1x3 + 0.5x4 = -1x + x3 + x + -1x3

Reorder the terms:
x + -0.5x2 + -1x3 + 0.5x4 = -1x + x + x3 + -1x3

Combine like terms: -1x + x = 0
x + -0.5x2 + -1x3 + 0.5x4 = 0 + x3 + -1x3
x + -0.5x2 + -1x3 + 0.5x4 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
x + -0.5x2 + -1x3 + 0.5x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -0.5x + -1x2 + 0.5x3) = 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 + -0.5x + -1x2 + 0.5x3)' equal to zero and attempt to solve:

Simplifying
1 + -0.5x + -1x2 + 0.5x3 = 0

Solving
1 + -0.5x + -1x2 + 0.5x3 = 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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