z^4-21z^2=0

Solution for z^4-21z^2=0 equation:

Simplifying
z4 + -21z2 = 0

Reorder the terms:
-21z2 + z4 = 0

Solving
-21z2 + z4 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
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 = {0, -4.582575695, 4.582575695}