3y^4-2y^2-5=0

Solution for 3y^4-2y^2-5=0 equation:

Simplifying
3y4 + -2y2 + -5 = 0

Reorder the terms:
-5 + -2y2 + 3y4 = 0

Solving
-5 + -2y2 + 3y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -1y2)(5 + -3y2) = 0

Subproblem 1
Set the factor '(-1 + -1y2)' equal to zero and attempt to solve:

Simplifying
-1 + -1y2 = 0

Solving
-1 + -1y2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1y2 = 0 + 1
-1y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1y2 = 1

Divide each side by '-1'.
y2 = -1

Simplifying
y2 = -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 + -3y2)' equal to zero and attempt to solve:

Simplifying
5 + -3y2 = 0

Solving
5 + -3y2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3y2 = 0 + -5
-3y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-3y2 = -5

Divide each side by '-3'.
y2 = 1.666666667

Simplifying
y2 = 1.666666667

Take the square root of each side:
y = {-1.290994449, 1.290994449}
Solution
y = {-1.290994449, 1.290994449}