4z^5=84z^3

Solution for 4z^5=84z^3 equation:

Simplifying
4z5 = 84z3

Solving
4z5 = 84z3

Solving for variable 'z'.

Reorder the terms:
-84z3 + 4z5 = 84z3 + -84z3

Combine like terms: 84z3 + -84z3 = 0
-84z3 + 4z5 = 0

Factor out the Greatest Common Factor (GCF), '4z3'.
4z3(-21 + z2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'z3' equal to zero and attempt to solve:

Simplifying
z3 = 0

Solving
z3 = 0

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

Simplifying
z3 = 0

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 '(-21 + z2)' equal to zero and attempt to solve:

Simplifying
-21 + z2 = 0

Solving
-21 + z2 = 0

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

Add '21' to each side of the equation.
-21 + 21 + z2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + z2 = 0 + 21
z2 = 0 + 21

Combine like terms: 0 + 21 = 21
z2 = 21

Simplifying
z2 = 21

Take the square root of each side:
z = {-4.582575695, 4.582575695}
Solution
z = {-4.582575695, 4.582575695}