Integer solutions to fraction equation

I am having trouble finding all solutions (or at least proving I have all the solutions already).

The equation is

$\frac{1}{a}+\frac{1}{b}+\frac{2}{c}=1$

*a,b,c are positive I tried to base it on the solutions of a similar equation with the last term a 1 instead of a 2.

I am having trouble finding all solutions (or at least proving I have all the solutions already).

The equation is

$\frac{1}{a}+\frac{1}{b}+\frac{2}{c}=1$

*a,b,c are positive I tried to base it on the solutions of a similar equation with the last term a 1 instead of a 2.