z^6+2z^3+1=0

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Solution for z^6+2z^3+1=0 equation: 


Simplifying
z6 + 2z3 + 1 = 0

Reorder the terms:
1 + 2z3 + z6 = 0

Solving
1 + 2z3 + z6 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + z3)(1 + z3) = 0


Subproblem 1
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.

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.

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