ax^2y=a^2xy

Solution for ax^2y=a^2xy equation:

Simplifying
ax2y = a2xy

Solving
ax2y = a2xy

Solving for variable 'a'.

Combine like terms: a2xy + -1a2xy = 0
ax2y + -1a2xy = 0

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

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

Simplifying
axy = 0

Solving
axy = 0

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

Simplifying
axy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(x + -1a)' equal to zero and attempt to solve:

Simplifying
x + -1a = 0

Reorder the terms:
-1a + x = 0

Solving
-1a + x = 0

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

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

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

Divide each side by '-1'.
a = x

Simplifying
a = x
Solution
a = {x}