As complex as the Trinity is to comprehend, it is nevertheless a fairly simple doctrine to understand and define. Do just a little bit of research into Christian doctrine and you will find that we believe there is one, and only one God, however that God is tripersonal, meaning He exists in 3 separate, yet co-equal persons. The Father is God, the Son, who became flesh through the virgin Mary, is God (Mary, by contrast, is definitely not divine), and the Holy Spirit is God.
Now, I understand why a Muslim might then come around and say "so you believe 1 + 1 + 1 = 1?". This is still not accurate. The correct equation would be either 1∞ + 1∞ + 1∞ = 1∞, or even just ∞ + ∞ + ∞ = ∞. Infinity, by definition, can neither be added to, nor subtracted from. As a result, if you have three co-equal eternal persons as one God, they're always going to be one eternal God. Nevertheless, as far as the Muslim understanding of the Trinity falls from the actual concept of the Trinity, it is ironically a lot closer to the Trinity than Allah and his prophet ever managed to get.
In the Qur'an, Christians are said to believe not in one God existing in three coequal persons, that being the Father, Son and Holy Spirit, but actually, 3 gods, with Jesus and His mother being taken as gods besides Allah. The concept of Allah as Father is completely alien in Islam, and at least as far as discussing the Trinity, the Holy Spirit seems to have gone missing. In His place, Mary is said to be worshipped.
If Muhammad was a false prophet, and Allah a mere idol, this makes perfect sense. Humans have a nasty tendency to talk past each other when it comes to religion, and lets be honest, when you look at Catholicism, they almost do seem to make Mary out to be a god. They even have the cheek to call Mary the "Mother of God", and as the Father is called the Father, and Jesus the Son, it would make sense to an illiterate 7th century caravan robber that Christians believe in some kind of divine family. God the Father slept with God the Mother to produce God the Son, there you go, you have the Islamic idea of the Holy Trinity. I have no issues seeing how Muhammad might have made that mistake.
But should Allah be so ignorant? Should we not expect a supposedly all knowing God to have at least a reasonable grasp on the most basic doctrines held by the religion he is addressing? Of course we should! It would make sense for Muhammad to make basic theological errors, but not Allah.
So there are only three possibilities here. The first is that Allah is actually not all knowing, or at least wasn't when he spoke to Muhammad. Instead, he is so ignorant that he knew less about Christianity than modern Muslims on the internet. But this is not how the Qur'an describes Allah.
The second possibility is that Allah actually does know what Christianity teaches, and yet he is deceptive. This is more in line with what Islam teaches, as the Qur'an teaches that Allah is the best of deceivers (Qur'an 3:54; 8:30). However, when you add an omnipotent, omniscient deceiver to your philosophy, you lose literally everything. You and I could be slugs right now, and Allah is just tricking us into thinking we're humans discussing theology. Even if such a deceiver existed, it would not be worth believing in him.
Which leaves us with the third possibility: "Allah" really is a deceiver, so much so that he is actually not even Allah. Whether Allah is Muhammad's own invention, or actually Satan, the fact that he incorrectly describes the doctrine of the Trinity shows that he is not the God preached by Moses and the prophets, or the Apostles, or by Christ Himself. In Christianity, God really is all knowing, and yet, He is also too holy to lie. Through His servant, Paul, He actually tells us that He cannot lie (Titus 1:2). Thus, it would be unimaginable to find a misrepresentation of any religion in the Bible.
As Islam would not exist for another 600 years, obviously the Bible does not attempt to directly address it. But let's suppose a new book was written today by someone claiming to be a prophet of God, who came to confirm the revelations that came before it. I would hope this would be the goal of any Christian author regardless of how they claim their book came to be, but suppose this person believed they were writing scripture. Yet, their book had a major flaw: When explaining that Muhammad was a false prophet, it claimed that he and his wife Aisha both claimed to be members of the Trinity. What Muslim would believe it? What Christian would believe it? If a Christian wrote that book in his own capacity, he'd be a laughing stock. If he claimed to be a prophet of God, we'd cast him out of the Church as a heretic.
How, then, can Muslims expect Christians to believe Muhammad was a prophet? Muhammad didn't know the most basic thing about Christian theology. As a general rule, if you're smarter than your god, your god isn't a god. My Muslim friends, I mean no disrespect to you, but Muhammad is a false prophet, Allah is an idol, and Islam is a fraud. When taken to the grave, it leads to a place both our religions tell us we do not want to go: The everlasting lake of fire.
So, what's the solution? You will be glad to know that God is far more merciful than Islam portrays Him. Rather than not loving the unbelievers, as Qur’an 3:31-32 says, the God of the Bible loves you so much that He has paid a heavy price for your salvation: The blood of His Son. When Jesus was crucified, He took the punishment for all the sins you have ever committed. Those common to all men, and those related to Islam. After He died, He rose again. By confessing Him as Lord (i.e. God, possessing all authority in Heaven and on Earth), turning from your sins, and believing He rose from the dead, all your sins will be forgiven. Every last one of them. Therefore, believe, and be baptised as a sign of good conscience towards God. Then you will receive eternal life.