What do the of Thebes want Oedipus to do for them?

If I remember correctly, Thebes was being threatened by a Sphinx and no one had been able to answer the riddle it required to leave them alone. Anyone who attempted to answer and failed was killed by the Sphinx. Oedipus said he would try to answer the riddle because he wanted to free the people of Thebes and obtain the reward the king was offering.