2y^4+6y^2-20=0

Solution for 2y^4+6y^2-20=0 equation:

Simplifying
2y4 + 6y2 + -20 = 0

Reorder the terms:
-20 + 6y2 + 2y4 = 0

Solving
-20 + 6y2 + 2y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 3y2 + y4) = 0

Factor a trinomial.
2((-5 + -1y2)(2 + -1y2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1y2)' equal to zero and attempt to solve:

Simplifying
-5 + -1y2 = 0

Solving
-5 + -1y2 = 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 + -1y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y2 = 0 + 5
-1y2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1y2 = 5

Divide each side by '-1'.
y2 = -5

Simplifying
y2 = -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 '(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

Take the square root of each side:
y = {-1.414213562, 1.414213562}
Solution
y = {-1.414213562, 1.414213562}