ax+ay=a

Solution for ax+ay=a equation:

Simplifying
ax + ay = a

Solving
ax + ay = a

Solving for variable 'a'.

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

Add '-1a' to each side of the equation.
ax + -1a + ay = a + -1a

Reorder the terms:
-1a + ax + ay = a + -1a

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(-1 + x + y) = 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 + x + y)' equal to zero and attempt to solve:

Simplifying
-1 + x + y = 0

Solving
-1 + x + y = 0

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

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

Reorder the terms:
-1 + 1 + x + y = 0 + 1

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

Combine like terms: 0 + 1 = 1
x + y = 1

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

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

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

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

Simplifying
0 = 1 + -1x + -1y

The solution to this equation could not be determined.

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