9Y^4-32Y^2-16=0

Solution for 9Y^4-32Y^2-16=0 equation:

Simplifying
9Y4 + -32Y2 + -16 = 0

Reorder the terms:
-16 + -32Y2 + 9Y4 = 0

Solving
-16 + -32Y2 + 9Y4 = 0

Solving for variable 'Y'.

Factor a trinomial.
(-4 + -9Y2)(4 + -1Y2) = 0

Factor a difference between two squares.
(-4 + -9Y2)((2 + Y)(2 + -1Y)) = 0

Subproblem 1
Set the factor '(-4 + -9Y2)' equal to zero and attempt to solve:

Simplifying
-4 + -9Y2 = 0

Solving
-4 + -9Y2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -9Y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -9Y2 = 0 + 4
-9Y2 = 0 + 4

Combine like terms: 0 + 4 = 4
-9Y2 = 4

Divide each side by '-9'.
Y2 = -0.4444444444

Simplifying
Y2 = -0.4444444444

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

Simplifying
2 + Y = 0

Solving
2 + Y = 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 + Y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + Y = 0 + -2
Y = 0 + -2

Combine like terms: 0 + -2 = -2
Y = -2

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

Simplifying
2 + -1Y = 0

Solving
2 + -1Y = 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 + -1Y = 0 + -2

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

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

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

Simplifying
Y = 2
Solution
Y = {-2, 2}