y^4+9y^2-36=0

Solution for y^4+9y^2-36=0 equation:

Simplifying
y4 + 9y2 + -36 = 0

Reorder the terms:
-36 + 9y2 + y4 = 0

Solving
-36 + 9y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-12 + -1y2)(3 + -1y2) = 0

Subproblem 1
Set the factor '(-12 + -1y2)' equal to zero and attempt to solve:

Simplifying
-12 + -1y2 = 0

Solving
-12 + -1y2 = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1y2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1y2 = 0 + 12
-1y2 = 0 + 12

Combine like terms: 0 + 12 = 12
-1y2 = 12

Divide each side by '-1'.
y2 = -12

Simplifying
y2 = -12

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 '(3 + -1y2)' equal to zero and attempt to solve:

Simplifying
3 + -1y2 = 0

Solving
3 + -1y2 = 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 + -1y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y2 = 0 + -3
-1y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1y2 = -3

Divide each side by '-1'.
y2 = 3

Simplifying
y2 = 3

Take the square root of each side:
y = {-1.732050808, 1.732050808}
Solution
y = {-1.732050808, 1.732050808}