What are the proofs for the intercession of the Messenger for those among the monotheists who committed major sins, and his intercession for people whose good deeds equal their bad deeds?

Among his intercessions (peace and blessings of Allah be upon him) on the Day of Resurrection are his intercession for the people of major sins from his nation, and his intercession for a people whose good deeds and evil deeds are equal, so that they may enter Paradise. The proof for this is his (peace and blessings of Allah be upon him) saying: "My intercession is for the people of major sins from my nation."