The three factions are the pro-slavery, anti-slavery, and neutral groups. It is obvious in their names what they stood for. The peaceful resolution ended with the compromise that a bicameral structure of the congress will be established to represent well the states with huge populations but without relying solely on population is the basis for representation.
The crucial compromise there that sacrificed the rights of African Americans in favor of a stronger union among the states exploded once more in 1819 when Missouri petitioned to join the United States as a slave state.
Southerners who opposed the Missouri Compromise did so because it set a precedent for Congress to make laws concerning slavery, while Northerners disliked the law because it meant slavery was expanded into new territory.