z^6+5z^3+6=0

Solution for z^6+5z^3+6=0 equation:

Simplifying
z6 + 5z3 + 6 = 0

Reorder the terms:
6 + 5z3 + z6 = 0

Solving
6 + 5z3 + z6 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z3)(2 + z3) = 0

Subproblem 1
Set the factor '(3 + z3)' equal to zero and attempt to solve:

Simplifying
3 + z3 = 0

Solving
3 + z3 = 0

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

Add '-3' to each side of the equation.
3 + -3 + z3 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z3 = 0 + -3
z3 = 0 + -3

Combine like terms: 0 + -3 = -3
z3 = -3

Simplifying
z3 = -3

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 '(2 + z3)' equal to zero and attempt to solve:

Simplifying
2 + z3 = 0

Solving
2 + z3 = 0

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

Add '-2' to each side of the equation.
2 + -2 + z3 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z3 = 0 + -2
z3 = 0 + -2

Combine like terms: 0 + -2 = -2
z3 = -2

Simplifying
z3 = -2

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.