4y^4-2y^2-2=0

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

Simplifying
4y4 + -2y2 + -2 = 0

Reorder the terms:
-2 + -2y2 + 4y4 = 0

Solving
-2 + -2y2 + 4y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -1y2 + 2y4) = 0

Factor a trinomial.
2((-1 + -2y2)(1 + -1y2)) = 0

Factor a difference between two squares.
2((-1 + -2y2)((1 + y)(1 + -1y))) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -2y2)' equal to zero and attempt to solve:

Simplifying
-1 + -2y2 = 0

Solving
-1 + -2y2 = 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 + -2y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2y2 = 0 + 1
-2y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2y2 = 1

Divide each side by '-2'.
y2 = -0.5

Simplifying
y2 = -0.5

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 '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 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 + y = 0 + -1

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

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

Simplifying
y = -1
Subproblem 3
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 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 + -1y = 0 + -1

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

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

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

Simplifying
y = 1
Solution
y = {-1, 1}