is it possible to solder stranded & solid wire together??
Short answer: yes.
How you do it will depend on the wires and the use.
You probably should not solder household wires (in wall sockets or lamps). I don’t know why but it’s just not done.
You may want to tin the end of the stranded wire before twisting it onto the solid. This makes the stranded a bit solider.(ouch!)
if the two wires are much different in size, you may end up twisting one around the other.
There are lots of diagrams in the wiring books.
David