0=-x^4+5x^3-5x^2+4x

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Solution for 0=-x^4+5x^3-5x^2+4x equation: 


Simplifying
0 = -1x4 + 5x3 + -5x2 + 4x

Reorder the terms:
0 = 4x + -5x2 + 5x3 + -1x4

Solving
0 = 4x + -5x2 + 5x3 + -1x4

Solving for variable 'x'.
Remove the zero:
-4x + 5x2 + -5x3 + x4 = 4x + -5x2 + 5x3 + -1x4 + -4x + 5x2 + -5x3 + x4

Reorder the terms:
-4x + 5x2 + -5x3 + x4 = 4x + -4x + -5x2 + 5x2 + 5x3 + -5x3 + -1x4 + x4

Combine like terms: 4x + -4x = 0
-4x + 5x2 + -5x3 + x4 = 0 + -5x2 + 5x2 + 5x3 + -5x3 + -1x4 + x4
-4x + 5x2 + -5x3 + x4 = -5x2 + 5x2 + 5x3 + -5x3 + -1x4 + x4

Combine like terms: -5x2 + 5x2 = 0
-4x + 5x2 + -5x3 + x4 = 0 + 5x3 + -5x3 + -1x4 + x4
-4x + 5x2 + -5x3 + x4 = 5x3 + -5x3 + -1x4 + x4

Combine like terms: 5x3 + -5x3 = 0
-4x + 5x2 + -5x3 + x4 = 0 + -1x4 + x4
-4x + 5x2 + -5x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
-4x + 5x2 + -5x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + 5x + -5x2 + 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 '(-4 + 5x + -5x2 + x3)' equal to zero and attempt to solve:

Simplifying
-4 + 5x + -5x2 + x3 = 0

Solving
-4 + 5x + -5x2 + 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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