Is the Trinity mentioned in the Bible?

I find it hard to imagine Jesus saying that he would be joining his father and the Holy Spirit to form a single operating unit. If it is not in the Bible then where did the idea originate?

I see the Trinity as solving a sticky problem. Jesus had in effect taken over the family business. Nobody prays to God the Father. He has no role to play in Christian holidays. But you can’t have God the Father go into retirement, so what’s to be done with him? Link him to Jesus, throw in the Holy Spirit to keep things from being too obvious, and say that there is some incomprehensible union among them. Problem solved.