How to solve the following equation depending on $a$,$b$,$c$?

Question

I need to find real numbers $a$,$b$,$c$ so $a+b+c-abc-2=0$. I know that it is true when $a=b=c=1$ but how do I know it does not have or have other solutions? Btw I have not found a tag for this question other that that.

Answer 1

There are many solutions. Take an example, Let $a=0$

The given equation becomes $b+c-2=0$ or $b+c=2$

Since negative and positive numbers are possible, there are infinite values possible for (b,c) for which the above equation holds.