=y^4-9y^2+20

Solution for =y^4-9y^2+20 equation:

Simplifying
0 = y4 + -9y2 + 20

Reorder the terms:
0 = 20 + -9y2 + y4

Solving
0 = 20 + -9y2 + y4

Solving for variable 'y'.

Combine like terms: 0 + -20 = -20
-20 + 9y2 + -1y4 = 20 + -9y2 + y4 + -20 + 9y2 + -1y4

Reorder the terms:
-20 + 9y2 + -1y4 = 20 + -20 + -9y2 + 9y2 + y4 + -1y4

Combine like terms: 20 + -20 = 0
-20 + 9y2 + -1y4 = 0 + -9y2 + 9y2 + y4 + -1y4
-20 + 9y2 + -1y4 = -9y2 + 9y2 + y4 + -1y4

Combine like terms: -9y2 + 9y2 = 0
-20 + 9y2 + -1y4 = 0 + y4 + -1y4
-20 + 9y2 + -1y4 = y4 + -1y4

Combine like terms: y4 + -1y4 = 0
-20 + 9y2 + -1y4 = 0

Factor a trinomial.
(-5 + y2)(4 + -1y2) = 0

Factor a difference between two squares.
(-5 + y2)((2 + y)(2 + -1y)) = 0

Subproblem 1
Set the factor '(-5 + y2)' equal to zero and attempt to solve:

Simplifying
-5 + y2 = 0

Solving
-5 + y2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + y2 = 0 + 5
y2 = 0 + 5

Combine like terms: 0 + 5 = 5
y2 = 5

Simplifying
y2 = 5

Take the square root of each side:
y = {-2.236067978, 2.236067978}
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 = {-2.236067978, 2.236067978, -2, 2}