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 + -1z3)(1 + -1z3) = 0

Subproblem 1

Set the factor '(1 + -1z3)' equal to zero and attempt to solve: Simplifying 1 + -1z3 = 0 Solving 1 + -1z3 = 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 + -1z3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z3 = 0 + -1 -1z3 = 0 + -1 Combine like terms: 0 + -1 = -1 -1z3 = -1 Divide each side by '-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 + -1z3)' equal to zero and attempt to solve: Simplifying 1 + -1z3 = 0 Solving 1 + -1z3 = 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 + -1z3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z3 = 0 + -1 -1z3 = 0 + -1 Combine like terms: 0 + -1 = -1 -1z3 = -1 Divide each side by '-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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