-21z^6=-7z^4

Solution for -21z^6=-7z^4 equation:

Simplifying
-21z6 = -7z4

Solving
-21z6 = -7z4

Solving for variable 'z'.

Reorder the terms:
7z4 + -21z6 = -7z4 + 7z4

Combine like terms: -7z4 + 7z4 = 0
7z4 + -21z6 = 0

Factor out the Greatest Common Factor (GCF), '7z4'.
7z4(1 + -3z2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'z4' equal to zero and attempt to solve:

Simplifying
z4 = 0

Solving
z4 = 0

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

Simplifying
z4 = 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 '(1 + -3z2)' equal to zero and attempt to solve:

Simplifying
1 + -3z2 = 0

Solving
1 + -3z2 = 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 + -3z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3z2 = 0 + -1
-3z2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3z2 = -1

Divide each side by '-3'.
z2 = 0.3333333333

Simplifying
z2 = 0.3333333333

Take the square root of each side:
z = {-0.577350269, 0.577350269}
Solution
z = {-0.577350269, 0.577350269}