y^4-2y+y=0

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

Simplifying
y4 + -2y + y = 0

Reorder the terms:
-2y + y + y4 = 0

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

Solving
-1y + y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1 + y3) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-1 + y3)' equal to zero and attempt to solve:

Simplifying
-1 + y3 = 0

Solving
-1 + y3 = 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 + y3 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + y3 = 0 + 1
y3 = 0 + 1

Combine like terms: 0 + 1 = 1
y3 = 1

Simplifying
y3 = 1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}