6s^4+s^2-5=0

Solution for 6s^4+s^2-5=0 equation:

Simplifying
6s4 + s2 + -5 = 0

Reorder the terms:
-5 + s2 + 6s4 = 0

Solving
-5 + s2 + 6s4 = 0

Solving for variable 's'.

Factor a trinomial.
(-1 + -1s2)(5 + -6s2) = 0

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

Simplifying
-1 + -1s2 = 0

Solving
-1 + -1s2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1s2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1s2 = 0 + 1
-1s2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1s2 = 1

Divide each side by '-1'.
s2 = -1

Simplifying
s2 = -1

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 '(5 + -6s2)' equal to zero and attempt to solve:

Simplifying
5 + -6s2 = 0

Solving
5 + -6s2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6s2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6s2 = 0 + -5
-6s2 = 0 + -5

Combine like terms: 0 + -5 = -5
-6s2 = -5

Divide each side by '-6'.
s2 = 0.8333333333

Simplifying
s2 = 0.8333333333

Take the square root of each side:
s = {-0.912870929, 0.912870929}
Solution
s = {-0.912870929, 0.912870929}