Pursue to a conclusion or bring to a successful issue(verb)
WordNet. Princeton University. 2010.
Use "follow out" in a sentence
"The indolence and prostration of the body produce a kind of activity in the mind, if that may properly be called activity which is merely giving loose to the imagination and the emotions as they follow out the wild train of incoherent thought, or are agitated by impulses of spontaneous and ungoverned feeling."
"Though Smith was a mere lad of sixteen at that time, his mind had already, under Hutcheson's stimulating instructions, begun to work effectively on the ideas lodged in it and to follow out their suggestions in his own thought."
"C. Bell did not attempt to follow out his views as far as they might have been carried."