2y^2=2y

Solution for 2y^2=2y equation:

Simplifying
2y2 = 2y

Solving
2y2 = 2y

Solving for variable 'y'.

Reorder the terms:
-2y + 2y2 = 2y + -2y

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

Factor out the Greatest Common Factor (GCF), '2y'.
2y(-1 + y) = 0

Ignore the factor 2.
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}