(a*(1-y))-(a*y)=0

Solution for (a*(1-y))-(a*y)=0 equation:

Simplifying
(a(1 + -1y)) + -1(a * y) = 0
((1 * a + -1y * a)) + -1(a * y) = 0
((1a + -1ay)) + -1(a * y) = 0
(1a + -1ay) + -1(a * y) = 0

Remove parenthesis around (1a + -1ay)
1a + -1ay + -1(a * y) = 0

Multiply a * y
1a + -1ay + -1(ay) = 0

Combine like terms: -1ay + -1ay = -2ay
1a + -2ay = 0

Solving
1a + -2ay = 0

Solving for variable 'a'.

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

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

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

Simplifying
a = 0

Solving
a = 0

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

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

Simplifying
1 + -2y = 0

Solving
1 + -2y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2y = 0 + -1

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

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

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

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

Simplifying
0 = -1 + 2y

The solution to this equation could not be determined.

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