z^7+6z^4-16z=0

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Solution for z^7+6z^4-16z=0 equation: 


Simplifying
z7 + 6z4 + -16z = 0

Reorder the terms:
-16z + 6z4 + z7 = 0

Solving
-16z + 6z4 + z7 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-16 + 6z3 + z6) = 0

Factor a trinomial.
z((-8 + -1z3)(2 + -1z3)) = 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 '(-8 + -1z3)' equal to zero and attempt to solve:

Simplifying
-8 + -1z3 = 0

Solving
-8 + -1z3 = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1z3 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1z3 = 0 + 8
-1z3 = 0 + 8

Combine like terms: 0 + 8 = 8
-1z3 = 8

Divide each side by '-1'.
z3 = -8

Simplifying
z3 = -8

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 '(2 + -1z3)' equal to zero and attempt to solve:

Simplifying
2 + -1z3 = 0

Solving
2 + -1z3 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z3 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z3 = 0 + -2
-1z3 = 0 + -2

Combine like terms: 0 + -2 = -2
-1z3 = -2

Divide each side by '-1'.
z3 = 2

Simplifying
z3 = 2

The solution to this equation could not be determined.

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

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