(x-y)(z-y)=axy

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Solution for (x-y)(z-y)=axy equation:


Simplifying
(x + -1y)(z + -1y) = axy

Reorder the terms:
(x + -1y)(-1y + z) = axy

Multiply (x + -1y) * (-1y + z)
(x(-1y + z) + -1y * (-1y + z)) = axy
((-1y * x + z * x) + -1y * (-1y + z)) = axy
((-1xy + xz) + -1y * (-1y + z)) = axy
(-1xy + xz + (-1y * -1y + z * -1y)) = axy

Reorder the terms:
(-1xy + xz + (-1yz + 1y2)) = axy
(-1xy + xz + (-1yz + 1y2)) = axy
(-1xy + xz + -1yz + 1y2) = axy

Solving
-1xy + xz + -1yz + 1y2 = axy

Solving for variable 'x'.

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

Add '-1axy' to each side of the equation.
-1xy + xz + -1yz + -1axy + 1y2 = axy + -1axy

Reorder the terms:
-1axy + -1xy + xz + -1yz + 1y2 = axy + -1axy

Combine like terms: axy + -1axy = 0
-1axy + -1xy + xz + -1yz + 1y2 = 0

Add 'yz' to each side of the equation.
-1axy + -1xy + xz + -1yz + yz + 1y2 = 0 + yz

Combine like terms: -1yz + yz = 0
-1axy + -1xy + xz + 0 + 1y2 = 0 + yz
-1axy + -1xy + xz + 1y2 = 0 + yz
Remove the zero:
-1axy + -1xy + xz + 1y2 = yz

Add '-1y2' to each side of the equation.
-1axy + -1xy + xz + 1y2 + -1y2 = yz + -1y2

Combine like terms: 1y2 + -1y2 = 0
-1axy + -1xy + xz + 0 = yz + -1y2
-1axy + -1xy + xz = yz + -1y2

Reorder the terms:
-1axy + -1xy + xz + -1yz + y2 = yz + -1yz + -1y2 + y2

Combine like terms: yz + -1yz = 0
-1axy + -1xy + xz + -1yz + y2 = 0 + -1y2 + y2
-1axy + -1xy + xz + -1yz + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-1axy + -1xy + xz + -1yz + y2 = 0

The solution to this equation could not be determined.

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