Where does “подготавливать” come from?

подготавливать (Russian) comes from Russian подгото́вить, from Russian под-, from Proto-Slavic podъ- — under-.

Ancestry of “подготавливать”, step by step

Step	Language	Word	Meaning
1	Russian	подгото́вить	—
2	Russian	под-	upwards; closer; adding
3	Proto-Slavic	podъ-	under-

подготавливать — Etymology, Origin & Word History | Etymology Explorer