z^7+2(z^4)+z=0

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

Simplifying
z7 + 2(z4) + z = 0

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

Solving
z + 2z4 + z7 = 0

Solving for variable 'z'.

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

Factor a trinomial.
z((1 + z3)(1 + z3)) = 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 + 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 3
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.
Solution
z = {0}