3z^4-2z^2-96=0

Solution for 3z^4-2z^2-96=0 equation:

Simplifying
3z4 + -2z2 + -96 = 0

Reorder the terms:
-96 + -2z2 + 3z4 = 0

Solving
-96 + -2z2 + 3z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(-16 + -3z2)(6 + -1z2) = 0

Subproblem 1
Set the factor '(-16 + -3z2)' equal to zero and attempt to solve:

Simplifying
-16 + -3z2 = 0

Solving
-16 + -3z2 = 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 + -3z2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3z2 = 0 + 16
-3z2 = 0 + 16

Combine like terms: 0 + 16 = 16
-3z2 = 16

Divide each side by '-3'.
z2 = -5.333333333

Simplifying
z2 = -5.333333333

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 '(6 + -1z2)' equal to zero and attempt to solve:

Simplifying
6 + -1z2 = 0

Solving
6 + -1z2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z2 = 0 + -6
-1z2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1z2 = -6

Divide each side by '-1'.
z2 = 6

Simplifying
z2 = 6

Take the square root of each side:
z = {-2.449489743, 2.449489743}
Solution
z = {-2.449489743, 2.449489743}