2=6-y^4

Solution for 2=6-y^4 equation:

Simplifying
2 = 6 + -1y4

Solving
2 = 6 + -1y4

Solving for variable 'y'.

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

Add 'y4' to each side of the equation.
2 + y4 = 6 + -1y4 + y4

Combine like terms: -1y4 + y4 = 0
2 + y4 = 6 + 0
2 + y4 = 6

Add '-2' to each side of the equation.
2 + -2 + y4 = 6 + -2

Combine like terms: 2 + -2 = 0
0 + y4 = 6 + -2
y4 = 6 + -2

Combine like terms: 6 + -2 = 4
y4 = 4

Simplifying
y4 = 4

Reorder the terms:
-4 + y4 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + y4 = 0

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

Subproblem 1
Set the factor '(2 + y2)' equal to zero and attempt to solve:

Simplifying
2 + y2 = 0

Solving
2 + y2 = 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 + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y2 = 0 + -2
y2 = 0 + -2

Combine like terms: 0 + -2 = -2
y2 = -2

Simplifying
y2 = -2

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 + y2)' equal to zero and attempt to solve:

Simplifying
-2 + y2 = 0

Solving
-2 + y2 = 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 + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + y2 = 0 + 2
y2 = 0 + 2

Combine like terms: 0 + 2 = 2
y2 = 2

Simplifying
y2 = 2

Take the square root of each side:
y = {-1.414213562, 1.414213562}
Solution
y = {-1.414213562, 1.414213562}