y^4-4y^2-1152=0

Solution for y^4-4y^2-1152=0 equation:

Simplifying
y4 + -4y2 + -1152 = 0

Reorder the terms:
-1152 + -4y2 + y4 = 0

Solving
-1152 + -4y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-32 + -1y2)(36 + -1y2) = 0

Factor a difference between two squares.
(-32 + -1y2)((6 + y)(6 + -1y)) = 0

Subproblem 1
Set the factor '(-32 + -1y2)' equal to zero and attempt to solve:

Simplifying
-32 + -1y2 = 0

Solving
-32 + -1y2 = 0

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

Add '32' to each side of the equation.
-32 + 32 + -1y2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1y2 = 0 + 32
-1y2 = 0 + 32

Combine like terms: 0 + 32 = 32
-1y2 = 32

Divide each side by '-1'.
y2 = -32

Simplifying
y2 = -32

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

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Subproblem 3
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-6, 6}