a(x+y)=y(a+z)

Solution for a(x+y)=y(a+z) equation:

Simplifying
a(x + y) = y(a + z)
(x * a + y * a) = y(a + z)
(ax + ay) = y(a + z)
ax + ay = (a * y + z * y)
ax + ay = (ay + yz)

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

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

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

Solving
ax = yz

Solving for variable 'a'.

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

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

Simplifying
a = x-1yz