y^4-15y^2-16=0

Solution for y^4-15y^2-16=0 equation:

Simplifying
y4 + -15y2 + -16 = 0

Reorder the terms:
-16 + -15y2 + y4 = 0

Solving
-16 + -15y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -1y2)(16 + -1y2) = 0

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

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

Simplifying
4 + y = 0

Solving
4 + y = 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 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Subproblem 3
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-4, 4}