4z^4-8z^2=

Solution for 4z^4-8z^2= equation:

Simplifying
4z4 + -8z2 = 0

Reorder the terms:
-8z2 + 4z4 = 0

Solving
-8z2 + 4z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z2'.
4z2(-2 + z2) = 0

Ignore the factor 4.
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 '(-2 + z2)' equal to zero and attempt to solve:

Simplifying
-2 + z2 = 0

Solving
-2 + z2 = 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 + z2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + z2 = 0 + 2
z2 = 0 + 2

Combine like terms: 0 + 2 = 2
z2 = 2

Simplifying
z2 = 2

Take the square root of each side:
z = {-1.414213562, 1.414213562}
Solution
z = {0, -1.414213562, 1.414213562}