4y^4-32y^2-36=0

Solution for 4y^4-32y^2-36=0 equation:

Simplifying
4y4 + -32y2 + -36 = 0

Reorder the terms:
-36 + -32y2 + 4y4 = 0

Solving
-36 + -32y2 + 4y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -8y2 + y4) = 0

Factor a trinomial.
4((-1 + -1y2)(9 + -1y2)) = 0

Factor a difference between two squares.
4((-1 + -1y2)((3 + y)(3 + -1y))) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -1y2)' equal to zero and attempt to solve:

Simplifying
-1 + -1y2 = 0

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

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

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

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

Simplifying
y2 = -1

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

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

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

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

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

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

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

Simplifying
y = 3
Solution
y = {-3, 3}