Complex sentence: Carol's film career lasted from the late 1920s into the 1930s, and when it ended she became a talent agent; one of her clients was Alan Ladd, to whom she was married from 1942 until his death in 1964.
Split into simpler sentences: Carol's film career lasted from the late 1920s into the 1930s; when it ended, she became a talent agent. The last of her three marriages was to one of her clients, Alan Ladd, from 1942 until his death in 1964.