Vi multiple searching

I used to vi editor as standard used. But I dont know how to do multiple searching....normally I able to search single words during vi.

for example:
1) vi filename.txt ( opening the file )
2) /wordthatiseek ( in vi editor i type this to search the words)

let say the /var/log/message file. i want to search line with date and some message
 example:
i want to search 20112007 and words 'failed'. what should i type after the '/'?

thanks