0=x^5-5x^4+20x^2

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Solution for 0=x^5-5x^4+20x^2 equation: 


Simplifying
0 = x5 + -5x4 + 20x2

Reorder the terms:
0 = 20x2 + -5x4 + x5

Solving
0 = 20x2 + -5x4 + x5

Solving for variable 'x'.
Remove the zero:
-20x2 + 5x4 + -1x5 = 20x2 + -5x4 + x5 + -20x2 + 5x4 + -1x5

Reorder the terms:
-20x2 + 5x4 + -1x5 = 20x2 + -20x2 + -5x4 + 5x4 + x5 + -1x5

Combine like terms: 20x2 + -20x2 = 0
-20x2 + 5x4 + -1x5 = 0 + -5x4 + 5x4 + x5 + -1x5
-20x2 + 5x4 + -1x5 = -5x4 + 5x4 + x5 + -1x5

Combine like terms: -5x4 + 5x4 = 0
-20x2 + 5x4 + -1x5 = 0 + x5 + -1x5
-20x2 + 5x4 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
-20x2 + 5x4 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-20 + 5x2 + -1x3) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-20 + 5x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
-20 + 5x2 + -1x3 = 0

Solving
-20 + 5x2 + -1x3 = 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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