v^2=v

Solution for v^2=v equation:

Simplifying
v2 = v

Solving
v2 = v

Solving for variable 'v'.

Reorder the terms:
-1v + v2 = v + -1v

Combine like terms: v + -1v = 0
-1v + v2 = 0

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

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

Simplifying
v = 0

Solving
v = 0

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

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

Simplifying
-1 + v = 0

Solving
-1 + v = 0

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

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

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

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

Simplifying
v = 1
Solution
v = {0, 1}