The product of two positive three-digit palindromes is 436995. What is their sum?

By the way, a palindrome is number that is read the same backwards and forwards: example: 1331, 7557, 131, 767, 454, etc..

This is what I have tried:

I realize that either a or c must be 5, for the product to end in a 5. Also I see that one or both of these numbers must be a factor of 9 and 3, but i'm not sure what to make of these observations.

I'm not exactly sure where to go from here. Help is appreciated.