Question

What are all the possible solutions to this equation?

x+y+z=xyz

Answer 1

I figured out there are at least 7 answers to this just by noticing 0=0 and the other 6 are represented by 1+2+3=1*2*3 which can rearranged 3! ways

Answer 2

But how can we solve this without just guessing?

Answer 3

you would just have to make general statements
but we could write a proof for it

Answer 4

THERE ARE ONLY 6 WAYS`