Determine all triplets (a,b,c) where a,b,c are positive integers such that:

a+b+c+ab+bc+ca = abc+1.

i 'm taking a hit and trial method for this question:

 here when i put the value in LHS  value of anyone is taking 1 and others 0 (a=1,b=0,c=0 etc...)

  then its value equates the value of RHS i.e 1.

   so the solutins may have :

  a=1,b=0,c=0;

  a=0,b=1,c=0;

  a=0,b=0,c=1;   [they all  may be solutions]

    plz approve the answer or send its original answer if different!!!! 

a,b,c are positive integers, so they cannot take value 0.

That's not the solution.