There are several NT Scriptures that cast doubt on the validity of the doctrine of the Trinity. So I think we need to look at them individually and in light of the Old Testament.
John 17:3
3 "And this is eternal life, that they may know Thee, the only true God, and Jesus Christ whom Thou hast sent. NAS
1st Corinthians 8:5-6
5 For even if there are so-called gods whether in heaven or on earth, as indeed there are many gods and many lords, 6 yet for us there is but one God, the Father, from whom are all things, and we exist for Him; and one Lord, Jesus Christ, by whom are all things, and we exist through Him.
NAS
Ephesians 4:4-8
4 There is one body and one Spirit, just as also you were called in one hope of your calling; 5 one Lord, one faith, one baptism, 6 one God and Father of all who is over all and through all and in all. 7 But to each one of us grace was given according to the measure of Christ's gift. 8 Therefore it says,
"When He ascended on high,
He led captive a host of captives,
And He gave gifts to men." NAS
1st Timothy 2:5-7
5 For there is one God, and one mediator also between God and men, the man Christ Jesus, 6 who gave Himself as a ransom for all, the testimony borne at the proper time. 7 And for this I was appointed a preacher and an apostle (I am telling the truth, I am not lying) as a teacher of the Gentiles in faith and truth. NAS
The usual rationale is to opine that Jesus and Paul don't really mean what they said and wrote, commentators tell us that both Jesus and Paul are comparing the one true triune God to false gods. However, is this opinion valid or is this opinion based on tradition?
Exodus 3:15
15 And God, furthermore, said to Moses, "Thus you shall say to the sons of Israel, 'The LORD, the God of your fathers, the God of Abraham, the God of Isaac, and the God of Jacob, has sent me to you.' This is My name forever, and this is My memorial-name to all generations. NAS
Numbers 23:19
19 "God is not a man, that He should lie,
Nor a son of man, that He should repent;
Has He said, and will He not do it?
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Deuteronomy 6:4-8
4 "Hear, O Israel! The LORD is our God, the LORD is one! 5 "And you shall love the LORD your God with all your heart and with all your soul and with all your might. 6 And these words, which I am commanding you today, shall be on your heart; 7 and you shall teach them diligently to your sons and shall talk of them when you sit in your house and when you walk by the way and when you lie down and when you rise up. 8 And you shall bind them as a sign on your hand and they shall be as frontals on your forehead. NAS
Isaiah 63:16
16 For Thou art our Father, though Abraham does not know us,
And Israel does not recognize us.
Thou, O LORD, art our Father,
Our Redeemer from of old is Thy name. NAS
Isaiah 64:8
8 But now, O LORD, Thou art our Father,
We are the clay, and Thou our potter;
And all of us are the work of Thy hand. NAS
Jeremiah 10:10
10 But the LORD is the true God;
He is the living God and the everlasting King.
At His wrath the earth quakes,
And the nations cannot endure His indignation. NAS
The foundation of Christianity (God's household) is the apostles and the prophets (Ephesians 2:20) so when commentators either ignore the prophets or rationalize what the prophets wrote their foundation is no longer one of rock but one of sand.
There is a verse in 1 John used by many Trinitarians to try to prove that Jesus is God.
1st John 5:18-21
18 We know that no one who is born of God sins; but He who was born of God keeps him and the evil one does not touch him. 19 We know that we are of God, and the whole world lies in the power of the evil one. 20 And we know that the Son of God has come, and has given us understanding, in order that we might know Him who is true, and we are in Him who is true, in His Son Jesus Christ. This is the true God and eternal life. 21 Little children, guard yourselves from idols. NAS
Since both the Father and the Son are mentioned in this section of 1 John, how do we determine if John is referring to God the Father or Jesus Christ? The answer is by referring to our foundation as well as what Jesus said in John 17:3. The LORD (which is Yehovah in Hebrew) is the only true God in the prophets. Also when we take all of John 17 into account we read that Jesus is in Him who is true, that He who is true is in Jesus and both the Father and the Son are in all true believers.
Since I have brought up John 17 lets look at a verse in this chapter that is also used to try to show that Jesus is God.
John 17:5
5 "And now, glorify Thou Me together with Thyself, Father, with the glory which I had with Thee before the world was. NAS
Does this verse prove the preexistence of the Son as God? Not when we go back to our foundation.
Isaiah 42:8
8 "I am the LORD, that is My name;
I will not give My glory to another,
Nor My praise to graven images. NAS
Now when we continue reading in John 17 we read:
John 17:22-23
22 "And the glory which Thou hast given Me I have given to them; that they may be one, just as We are one; 23 I in them, and Thou in Me, that they may be perfected in unity, that the world may know that Thou didst send Me, and didst love them, even as Thou didst love Me. NAS
So we either have a contradiction in Scripture or the interpretation put on John 17:5 is forced and incorrect.
Another interesting aspect of 1 John 5:20 is that not all Trinitarian commentators agree that the last sentence refers to Jesus Christ. They base this on how the Greek word "houtos" is used in other Scriptures. However, when we let the Bible explain the Bible it is clear there is but one true God the Father who anointed the man Jesus Christ to be our Savior and appointed Jesus Christ as King of kings and Lord of lords.