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

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

Simplifying
z6 + -2z3 + 2 = 0

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

Solving
2 + -2z3 + z6 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2z3 + -2 + z6 = 0 + -2

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

Combine like terms: 2 + -2 = 0
0 + -2z3 + z6 = 0 + -2
-2z3 + z6 = 0 + -2

Combine like terms: 0 + -2 = -2
-2z3 + z6 = -2

The z term is -2z3.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2z3 + 1 + z6 = -2 + 1

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

Combine like terms: -2 + 1 = -1
1 + -2z3 + z6 = -1

Factor a perfect square on the left side:
(z3 + -1)(z3 + -1) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.