z^4+6z^2+5=0

Solution for z^4+6z^2+5=0 equation:

Simplifying
z4 + 6z2 + 5 = 0

Reorder the terms:
5 + 6z2 + z4 = 0

Solving
5 + 6z2 + z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + z2)(1 + z2) = 0

Subproblem 1
Set the factor '(5 + z2)' equal to zero and attempt to solve:

Simplifying
5 + z2 = 0

Solving
5 + z2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + z2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z2 = 0 + -5
z2 = 0 + -5

Combine like terms: 0 + -5 = -5
z2 = -5

Simplifying
z2 = -5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
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.

The solution to this equation could not be determined.