3s^4-192=0

Solution for 3s^4-192=0 equation:

Simplifying
3s4 + -192 = 0

Reorder the terms:
-192 + 3s4 = 0

Solving
-192 + 3s4 = 0

Solving for variable 's'.

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

Add '192' to each side of the equation.
-192 + 192 + 3s4 = 0 + 192

Combine like terms: -192 + 192 = 0
0 + 3s4 = 0 + 192
3s4 = 0 + 192

Combine like terms: 0 + 192 = 192
3s4 = 192

Divide each side by '3'.
s4 = 64

Simplifying
s4 = 64

Reorder the terms:
-64 + s4 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + s4 = 0

Factor a difference between two squares.
(8 + s2)(-8 + s2) = 0

Subproblem 1
Set the factor '(8 + s2)' equal to zero and attempt to solve:

Simplifying
8 + s2 = 0

Solving
8 + s2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + s2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + s2 = 0 + -8
s2 = 0 + -8

Combine like terms: 0 + -8 = -8
s2 = -8

Simplifying
s2 = -8

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 '(-8 + s2)' equal to zero and attempt to solve:

Simplifying
-8 + s2 = 0

Solving
-8 + s2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + s2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + s2 = 0 + 8
s2 = 0 + 8

Combine like terms: 0 + 8 = 8
s2 = 8

Simplifying
s2 = 8

Take the square root of each side:
s = {-2.828427125, 2.828427125}
Solution
s = {-2.828427125, 2.828427125}