y^4-6y^2-27=0

Solution for y^4-6y^2-27=0 equation:

Simplifying
y4 + -6y2 + -27 = 0

Reorder the terms:
-27 + -6y2 + y4 = 0

Solving
-27 + -6y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -1y2)(9 + -1y2) = 0

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

Subproblem 1
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

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}