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

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

Simplifying
z7 + 2(z4) + 4z = 0

Reorder the terms:
4z + 2z4 + z7 = 0

Solving
4z + 2z4 + z7 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(4 + 2z3 + z6) = 0

Subproblem 1Set 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 2Set the factor '(4 + 2z3 + z6)' equal to zero and attempt to solve:

Simplifying
4 + 2z3 + z6 = 0

Solving
4 + 2z3 + z6 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 2z3 + -4 + z6 = 0 + -4

Reorder the terms:
4 + -4 + 2z3 + z6 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 2z3 + z6 = 0 + -4
2z3 + z6 = 0 + -4

Combine like terms: 0 + -4 = -4
2z3 + z6 = -4

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 = -4 + 1

Reorder the terms:
1 + 2z3 + z6 = -4 + 1

Combine like terms: -4 + 1 = -3
1 + 2z3 + z6 = -3

Factor a perfect square on the left side:
(z3 + 1)(z3 + 1) = -3

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.Solutionz = {0}`