y^4+4y^2-117=0

Solution for y^4+4y^2-117=0 equation:

Simplifying
y4 + 4y2 + -117 = 0

Reorder the terms:
-117 + 4y2 + y4 = 0

Solving
-117 + 4y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-13 + -1y2)(9 + -1y2) = 0

Factor a difference between two squares.
(-13 + -1y2)((3 + y)(3 + -1y)) = 0

Subproblem 1
Set the factor '(-13 + -1y2)' equal to zero and attempt to solve:

Simplifying
-13 + -1y2 = 0

Solving
-13 + -1y2 = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1y2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1y2 = 0 + 13
-1y2 = 0 + 13

Combine like terms: 0 + 13 = 13
-1y2 = 13

Divide each side by '-1'.
y2 = -13

Simplifying
y2 = -13

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}