At The First Council of Nicea: The first council of Nicea (Nicaea) came to an end on August 25, 325 A.D. Lasting two months (perhaps having begun on May 20), and held in Bithynia, the First Council of Nicea was attended by 318 Church Fathers.
Opposing Images of God: Trinitarian Church fathers, Bishop Alexander of Alexandria and his deacon Athanasius, believed there were three persons in one god. The Trinitarians were pitted against the Monarchianists, who believed in only one indivisible god. These included Arius, Presbyter in Alexandria, and Eusebius, Bishop of Nicomedia.
Homo Ousion (same substance) vs. Homoi Ousion (like substance): The sticking point at the Nicene Council was a concept found nowhere in the Bible: homoousion. According to the concept of homo-ousion, Christ the Son was con-substantial (sharing the same substance) with the Father. Arius and Eusebius disagreed. Arius thought the Father, Son, and Holy Spirit were materially separate from each other, and that the Father created the Son.
Arius and his followers, the Arians, believed if the Son were equal to the Father, there would be more than one God. The opposing Trinitarians believed it diminished the importance of the Son to make him subordinate to the Father.
Wavering Decision of Constantine: The Trinitarian bishops prevailed. Emperor Constantine was not himself a Christian. Despite this, he had recently made Christianity free religion of the Roman Empire. This made heresy akin to revolt, so Constantine exiled the excommunicated Arius to Illyria.
Constantine's friend Eusebius, who eventually withdrew his objection, but still wouldn't sign the statement of faith, and a neighboring bishop, Theognis, were also exiled -- to Gaul. Constantine reversed his opinion about the Arian heresy, and had both exiled bishops reinstated three years later (in 328). At the same time, Arius was recalled from exile.
Constantine's sister and Eusebius worked on the emperor to obtain reinstatement for Arius, and they would have succeeded, if Arius hadn't suddenly died - by poisoning, probably, or, as some prefer to believe, by divine intervention.
Arianism regained momentum and survived until the reigns of Gratian and Theodosius, at which time, St. Ambrose set to work stamping it out.
St. Athanasius - Four Discourses Against the Arians: 'The essences of the Father and the Son and the Holy Ghost, are separate in nature, and estranged, and disconnected, and alien.'