3z^4-768z^2=

Solution for 3z^4-768z^2= equation:

Simplifying
3z4 + -768z2 = 0

Reorder the terms:
-768z2 + 3z4 = 0

Solving
-768z2 + 3z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z2'.
3z2(-256 + z2) = 0

Factor a difference between two squares.
3z2((16 + z)(-16 + z)) = 0

Ignore the factor 3.
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 '(16 + z)' equal to zero and attempt to solve:

Simplifying
16 + z = 0

Solving
16 + z = 0

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

Add '-16' to each side of the equation.
16 + -16 + z = 0 + -16

Combine like terms: 16 + -16 = 0
0 + z = 0 + -16
z = 0 + -16

Combine like terms: 0 + -16 = -16
z = -16

Simplifying
z = -16
Subproblem 3
Set the factor '(-16 + z)' equal to zero and attempt to solve:

Simplifying
-16 + z = 0

Solving
-16 + z = 0

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

Add '16' to each side of the equation.
-16 + 16 + z = 0 + 16

Combine like terms: -16 + 16 = 0
0 + z = 0 + 16
z = 0 + 16

Combine like terms: 0 + 16 = 16
z = 16

Simplifying
z = 16
Solution
z = {0, -16, 16}