Conversation so far:
When did David Letterman move to LA?
In 1975, encouraged by his then-wife Michelle and several of his Sigma Chi fraternity brothers, David Letterman moved to Los Angeles, California.
Why did David Letterman's fraternity brothers and then-wife Michelle encourage him to move to Los Angeles?
David Letterman moved to Los Angeles, California, with hope of becoming a comedy writer.

Question: What did he do when he got to LA?
Self-contained rewrite: What did David Letterman do when he got to Los Angeles?