Solution of the machine equation

In one of the first machines created by McCulloch, there were only two rules for generating a new number from a given one, consisting of the digits $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, and regarding the admissibility of numbers:

1. For any (possibly even empty) number $X$, the number $2X$ (here and elsewhere, $NM$ denotes the concatenation of the records of numbers $N$ and $M$) is admissible, and $2X$ generates the number $X$. 2. For any admissible number $X$, the number $3X$ is also admissible. If $X$ generates the number $Y$, then $3X$ generates the associate of number $Y$, that is, the number $Y2Y$.

McCulloch often challenged Inspector Craig with problems related to this machine. These problems provided two expressions S_1(X) and S_2(X), in each of which some part of $X$ could appear (possibly more than once) as a substring. The task required finding such a value of $X$ that S_1(X) would be an admissible number, which, when input into the machine, generates the number S_2(X). The inspector asks for your help to write a program that will find the desired number $X$.