x*a+y*(a-1)=z

Solution for x*a+y*(a-1)=z equation:

Simplifying
x * a + y(a + -1) = z

Multiply x * a
ax + y(a + -1) = z

Reorder the terms:
ax + y(-1 + a) = z
ax + (-1 * y + a * y) = z

Reorder the terms:
ax + (ay + -1y) = z
ax + (ay + -1y) = z

Solving
ax + ay + -1y = z

Solving for variable 'a'.

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

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

Combine like terms: -1y + y = 0
ax + ay + 0 = y + z
ax + ay = y + z

Reorder the terms:
ax + ay + -1y + -1z = y + -1y + z + -1z

Combine like terms: y + -1y = 0
ax + ay + -1y + -1z = 0 + z + -1z
ax + ay + -1y + -1z = z + -1z

Combine like terms: z + -1z = 0
ax + ay + -1y + -1z = 0

The solution to this equation could not be determined.