Complex sentence: As part of this compromise, Maine (formerly a part of Massachusetts) was admitted as a free state, of course, in order to maintain the balance of power in the U.S. Senate between the free states and the slaveholding states.
Split into simpler sentences: As part of this compromise, Maine (formerly a part of Massachusetts) was admitted as a free state. This addition maintained the balance of power in the U.S. Senate between the free states and the slaveholding states.