y^4-21y^2+108=0

Solution for y^4-21y^2+108=0 equation:

Simplifying
y4 + -21y2 + 108 = 0

Reorder the terms:
108 + -21y2 + y4 = 0

Solving
108 + -21y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(9 + -1y2)(12 + -1y2) = 0

Factor a difference between two squares.
((3 + y)(3 + -1y))(12 + -1y2) = 0

Subproblem 1
Set the factor '(12 + -1y2)' equal to zero and attempt to solve:

Simplifying
12 + -1y2 = 0

Solving
12 + -1y2 = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1y2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1y2 = 0 + -12
-1y2 = 0 + -12

Combine like terms: 0 + -12 = -12
-1y2 = -12

Divide each side by '-1'.
y2 = 12

Simplifying
y2 = 12

Take the square root of each side:
y = {-3.464101615, 3.464101615}
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 = {-3.464101615, 3.464101615, -3, 3}