-120x+20x^3-x^5=0

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Solution for -120x+20x^3-x^5=0 equation: 


Simplifying
-120x + 20x3 + -1x5 = 0

Solving
-120x + 20x3 + -1x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-120 + 20x2 + -1x4) = 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 '(-120 + 20x2 + -1x4)' equal to zero and attempt to solve:

Simplifying
-120 + 20x2 + -1x4 = 0

Solving
-120 + 20x2 + -1x4 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
120 + -20x2 + x4 = 0

Move the constant term to the right:

Add '-120' to each side of the equation.
120 + -20x2 + -120 + x4 = 0 + -120

Reorder the terms:
120 + -120 + -20x2 + x4 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -20x2 + x4 = 0 + -120
-20x2 + x4 = 0 + -120

Combine like terms: 0 + -120 = -120
-20x2 + x4 = -120

The x term is -20x2.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x2 + 100 + x4 = -120 + 100

Reorder the terms:
100 + -20x2 + x4 = -120 + 100

Combine like terms: -120 + 100 = -20
100 + -20x2 + x4 = -20

Factor a perfect square on the left side:
(x2 + -10)(x2 + -10) = -20

Can't calculate square root of the right side.

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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