y^4+32y^2-144=0

Solution for y^4+32y^2-144=0 equation:

Simplifying
y4 + 32y2 + -144 = 0

Reorder the terms:
-144 + 32y2 + y4 = 0

Solving
-144 + 32y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-36 + -1y2)(4 + -1y2) = 0

Factor a difference between two squares.
(-36 + -1y2)((2 + y)(2 + -1y)) = 0

Subproblem 1
Set the factor '(-36 + -1y2)' equal to zero and attempt to solve:

Simplifying
-36 + -1y2 = 0

Solving
-36 + -1y2 = 0

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

Add '36' to each side of the equation.
-36 + 36 + -1y2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1y2 = 0 + 36
-1y2 = 0 + 36

Combine like terms: 0 + 36 = 36
-1y2 = 36

Divide each side by '-1'.
y2 = -36

Simplifying
y2 = -36

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}