2z^7-2z^4+z=0

Solution for 2z^7-2z^4+z=0 equation:

Simplifying
2z7 + -2z4 + z = 0

Reorder the terms:
z + -2z4 + 2z7 = 0

Solving
z + -2z4 + 2z7 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(1 + -2z3 + 2z6) = 0

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(1 + -2z3 + 2z6)' equal to zero and attempt to solve:

Simplifying
1 + -2z3 + 2z6 = 0

Solving
1 + -2z3 + 2z6 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.5 + -1z3 + z6 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1z3 + -0.5 + z6 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1z3 + z6 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1z3 + z6 = 0 + -0.5
-1z3 + z6 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1z3 + z6 = -0.5

The z term is -1z3.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1z3 + 0.25 + z6 = -0.5 + 0.25

Reorder the terms:
0.25 + -1z3 + z6 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + -1z3 + z6 = -0.25

Factor a perfect square on the left side:
(z3 + -0.5)(z3 + -0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
z = {0}