Why is not possible? It can prove that IT WORKS.

I can prove from x-3=0, that x=0 & 3.

Multiply both sides by x to get x^2-3x=0

x=0

Whenever you multiply both sides of an equation by x, you are introducing x = 0 as a solution to the equation, because if x does = 0, you are multiplying both sides of the equation by 0, which makes even wrong equations true.

Example: Start with 3 = 2 (no solution).

Multiply by x on both sides

3x = 2x
x = 0

From an equation that had no solution you introduced x = 0. Be careful when multiplying by x.

Since x-3 = 0, x(x-3) = 0, so x = 0 OR (x-3) = 0. From an equation of the form ab = 0, we can infer only that a OR b is 0, not both. In this case, x = 0 does not work (x-3 isn't 0), so (x-3) = 0 and x=3.

It depends on who you tell this to An engineer would agree with you but a mathematician will want to hang you.