z^5+5z^3+4z=0

Solution for z^5+5z^3+4z=0 equation:

Simplifying
z5 + 5z3 + 4z = 0

Reorder the terms:
4z + 5z3 + z5 = 0

Solving
4z + 5z3 + z5 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(4 + 5z2 + z4) = 0

Factor a trinomial.
z((4 + z2)(1 + z2)) = 0

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

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(4 + z2)' equal to zero and attempt to solve:

Simplifying
4 + z2 = 0

Solving
4 + z2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z2 = 0 + -4
z2 = 0 + -4

Combine like terms: 0 + -4 = -4
z2 = -4

Simplifying
z2 = -4

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 + z2)' equal to zero and attempt to solve:

Simplifying
1 + z2 = 0

Solving
1 + z2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + z2 = 0 + -1
z2 = 0 + -1

Combine like terms: 0 + -1 = -1
z2 = -1

Simplifying
z2 = -1

The solution to this equation could not be determined.

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