z^6+4z^3+3=0

Solution for z^6+4z^3+3=0 equation:

Simplifying
z6 + 4z3 + 3 = 0

Reorder the terms:
3 + 4z3 + z6 = 0

Solving
3 + 4z3 + z6 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z3)(1 + 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 '(1 + z3)' equal to zero and attempt to solve:

Simplifying
1 + z3 = 0

Solving
1 + z3 = 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 + z3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + z3 = 0 + -1
z3 = 0 + -1

Combine like terms: 0 + -1 = -1
z3 = -1

Simplifying
z3 = -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.