3Y^4+3Y^2-6=0

Solution for 3Y^4+3Y^2-6=0 equation:

Simplifying
3Y4 + 3Y2 + -6 = 0

Reorder the terms:
-6 + 3Y2 + 3Y4 = 0

Solving
-6 + 3Y2 + 3Y4 = 0

Solving for variable 'Y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + Y2 + Y4) = 0

Factor a trinomial.
3((-2 + -1Y2)(1 + -1Y2)) = 0

Factor a difference between two squares.
3((-2 + -1Y2)((1 + Y)(1 + -1Y))) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1Y2)' equal to zero and attempt to solve:

Simplifying
-2 + -1Y2 = 0

Solving
-2 + -1Y2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1Y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1Y2 = 0 + 2
-1Y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1Y2 = 2

Divide each side by '-1'.
Y2 = -2

Simplifying
Y2 = -2

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}