x^4-x^3=x^2+x

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


Simplifying
x4 + -1x3 = x2 + x

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

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

Solving
-1x3 + x4 = x + x2

Solving for variable 'x'.

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

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

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

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

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

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

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