y^4-6y^2+5=0

Solution for y^4-6y^2+5=0 equation:

Simplifying
y4 + -6y2 + 5 = 0

Reorder the terms:
5 + -6y2 + y4 = 0

Solving
5 + -6y2 + y4 = 0

Solving for variable 'y'.

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

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

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

Simplifying
5 + -1y2 = 0

Solving
5 + -1y2 = 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 + -1y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y2 = 0 + -5
-1y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1y2 = -5

Divide each side by '-1'.
y2 = 5

Simplifying
y2 = 5

Take the square root of each side:
y = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-2.236067978, 2.236067978, -1, 1}