The word ‘Trinity’ is not found in Scripture. Yet, the concept behind it is very clearly Scriptural although some find it hard to comprehend. It is based on the following facts:
There is one God.
“Hear, O Israel! The Lord is our God, the Lord is one! (Deuteronomy 6:4, NASB)
The Father is fully God.
Do not work for the food which perishes, but for the food which endures to eternal life, which the Son of Man will give to you, for on Him the Father, God, has set His seal.” (John 6:27, NASB)
The Son (Jesus) is fully God.
In the beginning was the Word, and the Word was with God, and the Word was God. (John 1:1, NASB)
Read my long article on this (Link)
The Holy Spirit is fully God.
But Peter said, “Ananias, why has Satan filled your heart to lie to the Holy Spirit and to keep back some of the price of the land? While it remained unsold, did it not remain your own? And after it was sold, was it not under your control? Why is it that you have conceived this deed in your heart? You have not lied to men but to God.” (Acts 5:3-4, NASB)
The Father is not the Son.
But even if I do judge, My judgment is true; for I am not alone in it, but I and the Father who sent Me. Even in your law it has been written that the testimony of two men is true. I am He who testifies about Myself, and the Father who sent Me testifies about Me.” (John 8:16-18, NASB)
The Father is not the Holy Spirit
When the Helper comes, whom I will send to you from the Father, that is the Spirit of truth who proceeds from the Father, He will testify about Me, (John 15:26, NASB)
The Son is not the Holy Spirit.
and the Holy Spirit descended upon Him in bodily form like a dove, and a voice came out of heaven, “You are My beloved Son, in You I am well-pleased.” (Luke 3:22, NASB)
A brilliant article defending the doctrine of the Trinity can be found at the following link (Link). Go to that article for a more thorough explanation, this is just a quick article.
Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit, (Matthew 28:19, NASB)