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

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

Simplifying
0 = x5 + 2x3 + x

Reorder the terms:
0 = x + 2x3 + x5

Solving
0 = x + 2x3 + x5

Solving for variable 'x'.
Remove the zero:
-1x + -2x3 + -1x5 = x + 2x3 + x5 + -1x + -2x3 + -1x5

Reorder the terms:
-1x + -2x3 + -1x5 = x + -1x + 2x3 + -2x3 + x5 + -1x5

Combine like terms: x + -1x = 0
-1x + -2x3 + -1x5 = 0 + 2x3 + -2x3 + x5 + -1x5
-1x + -2x3 + -1x5 = 2x3 + -2x3 + x5 + -1x5

Combine like terms: 2x3 + -2x3 = 0
-1x + -2x3 + -1x5 = 0 + x5 + -1x5
-1x + -2x3 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
-1x + -2x3 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(1 + 2x2 + x4) = 0

Factor a trinomial.
-1x((1 + x2)(1 + x2)) = 0

Ignore the factor -1.
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 + x2)' equal to zero and attempt to solve:

Simplifying
1 + x2 = 0

Solving
1 + x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 0 + -1
x2 = 0 + -1

Combine like terms: 0 + -1 = -1
x2 = -1

Simplifying
x2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + x2)' equal to zero and attempt to solve:

Simplifying
1 + x2 = 0

Solving
1 + x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 0 + -1
x2 = 0 + -1

Combine like terms: 0 + -1 = -1
x2 = -1

Simplifying
x2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}