Smallest Multiple to "Palindromize" Goal:
Given any non-zero natural number a, find the smallest non-zero natural
number b such that a•b is palindromic, e.g. it reads the same forwards and backwards. Input a through any reasonable means (STDIN, function argument, etc.), And output b through any reasonable means (STDOUT, function return value.)
Notes:

Input will not always have a solution (multiples of 10), so you must create an error, or display -1/0

Input validation is not necessary, assume a is a natural number.

Standard loopholes apply (Hardcoding, using a language created after this challenge)


Examples:
a=34, b=8 (272)
a=628, b=78 (48984)
a=15, b=35 (525)
a=33, b=1 (33)
a=20, (Error, -1, or 0)
Pyth, 10 9 bytes
&amp;eQf_I`*Q

Try it online.
Explanation
&amp;eQf_I`*QT    Implicitly append T, and take input in Q. 
 eQ           Calculate input mod 10.
&amp;             Logical and, only evaluate the following if result ≠ 0.
   f          Starting from 1, find the first integer T for which... 
      `       ...the string representation of... 
       *QT    ...input multiplied by T... 
    _I        ...is equal to its reverse.