I had to mull over this for a bit before I came to a solution, and it wasn't a very satisfactory solution either.

Constantine was aiming for neither side during the Council of Nicaea in 325. He just wanted consensus. Eusebius casts this as a "Constantine the Great Mediator" as we can see here in what Eusebius recorded as Constantine's address to the Council:

"It was once my chief desire, dearest friends, to enjoy the spectacle of your united presence; and now that this desire is fulfilled, I feel myself bound to render thanks to God the universal King, because, in addition to all his other benefits, he has granted me a blessing higher than all the rest, in permitting me to see you not only all assembled together, but all united in a common harmony of sentiment. I pray therefore that no malignant adversary may henceforth interfere to mar our happy state; I pray that, now the impious hostility of the tyrants has been forever removed by the power of God our Saviour, that spirit who delights in evil may devise no other means for exposing the divine law to blasphemous calumny; for, in my judgment, internal strife within the Church of God, is far more evil and dangerous than any kind of war or conflict; and thus our differences appear to me more grievous than any outward trouble.

Accordingly, when, by the will and with the co-operation of God, I had been victorious over my enemies, I thought that nothing more remained but to render thanks to him, and sympathize in the joy of those whom he had restored to freedom through my instrumentality; as soon as I heard that intelligence which I had least expected to receive, I mean the news of your dissension, I judged it to be of no secondary importance, but with the earnest desire that a remedy for this evil also might be found through my means, I immediately sent to require your presence. And now I rejoice in beholding your assembly; but I feel that my desires will be most completely fulfilled when I can see you all united in one judgment, and that common spirit of peace and concord prevailing amongst you all, which it becomes you, as consecrated to the service of God, to commend to others. Delay not, then, dear friends: delay not, ye ministers of God, and faithful servants of him who is our common Lord and Saviour: begin from this moment to discard the causes of that division which has existed among you, and remove the perplexities of controversy by embracing the principles of peace. For by such conduct you will at the same time be acting in a manner most pleasing to the supreme God, and you will confer an exceeding favor on me who am your fellow-servant" (Eusebius, VC, 3.12)

And the consensus was homoousios. The First Nicaean Creed states: "And in one Lord Jesus Christ, the Son of God, begotten of the Father the only-begotten; that is, of the essence of the Father, God of God, Light of Light, very God of very God, begotten, not made, being of one substance [homoousios] with the Father."

After the consensus had been made, the bishops were forced to sign, and those dissidents who refused were pushed into exile. Eusebius writes of a Constantine triumphant at this feat, saying, "The result was that they were not only united as concerning the faith, but that the time for the celebration of the salutary feast of Easter was agreed on by all. Those points also which were sanctioned by the resolution of the whole body were committed to writing, and received the signature of each several member. Then the emperor, believing that he had thus obtained a second victory over the adversarsies of the Church, proceeded to offer a triumphal festival in honor of God" (Eus., VC, 3.14).

But herein lies the problem. Homoousius by the time of Constantine could have been interpreted as a legacy of Sabellius' Modal Monarchianism, which is what your professor may have been referring to. The best way to know, however, is to ask your professor himself :)