a(x+y)-a(x-y)=2ax

Solution for a(x+y)-a(x-y)=2ax equation:

Simplifying
a(x + y) + -1a(x + -1y) = 2ax
(x * a + y * a) + -1a(x + -1y) = 2ax
(ax + ay) + -1a(x + -1y) = 2ax
ax + ay + (x * -1a + -1y * -1a) = 2ax
ax + ay + (-1ax + 1ay) = 2ax

Reorder the terms:
ax + -1ax + ay + 1ay = 2ax

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

Combine like terms: ay + 1ay = 2ay
2ay = 2ax

Solving
2ay = 2ax

Solving for variable 'a'.

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

Add '-2ax' to each side of the equation.
-2ax + 2ay = 2ax + -2ax

Combine like terms: 2ax + -2ax = 0
-2ax + 2ay = 0

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

Ignore the factor 2.
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 '(-1x + y)' equal to zero and attempt to solve:

Simplifying
-1x + y = 0

Solving
-1x + y = 0

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

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

Combine like terms: -1x + x = 0
0 + y = 0 + x
y = 0 + x
Remove the zero:
y = x

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

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

Simplifying
0 = x + -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}