0=y-y^2

Solution for 0=y-y^2 equation:

Simplifying
0 = y + -1y2

Solving
0 = y + -1y2

Solving for variable 'y'.
Remove the zero:
-1y + y2 = y + -1y2 + -1y + y2

Reorder the terms:
-1y + y2 = y + -1y + -1y2 + y2

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

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

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