2y^4-11y^2-21=0

Solution for 2y^4-11y^2-21=0 equation:

Simplifying
2y4 + -11y2 + -21 = 0

Reorder the terms:
-21 + -11y2 + 2y4 = 0

Solving
-21 + -11y2 + 2y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -2y2)(7 + -1y2) = 0

Subproblem 1
Set the factor '(-3 + -2y2)' equal to zero and attempt to solve:

Simplifying
-3 + -2y2 = 0

Solving
-3 + -2y2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2y2 = 0 + 3
-2y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2y2 = 3

Divide each side by '-2'.
y2 = -1.5

Simplifying
y2 = -1.5

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 '(7 + -1y2)' equal to zero and attempt to solve:

Simplifying
7 + -1y2 = 0

Solving
7 + -1y2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y2 = 0 + -7
-1y2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1y2 = -7

Divide each side by '-1'.
y2 = 7

Simplifying
y2 = 7

Take the square root of each side:
y = {-2.645751311, 2.645751311}
Solution
y = {-2.645751311, 2.645751311}