The perceived confusion between the synoptic gospels and the account by St. John lies with the OBSERVATION of the Feast of Unleavened Bread and the Feast of Unleavened Bread. That is, the Law of Moses discriminates between the 14th of Nisan from the 15th of Nisan.
Exodus 12:17-18 (NASB)
17 You shall also observe the Feast of Unleavened Bread, for on this very day I brought your hosts out of the land of Egypt; therefore you shall observe this day throughout your generations as a permanent ordinance. 18 In the first month, on the fourteenth day of the month at evening, you shall eat unleavened bread, until the twenty-first day of the month at evening.
The OBSERVATION of the Feast of Unleavened Bread is commanded on the 14th of Nisan. Thus there are EIGHT days until the 21st of Nisan, when the feast concludes.
Leviticus 23:6 (NASB)
6 Then on the fifteenth day of the same month there is the Feast of Unleavened Bread to the Lord; for seven days you shall eat unleavened bread.
The Feast begins on the 15th of Nisan. Thus there are SEVEN days until the 21st of Nisan, when the feast concludes.
In other words, the synoptic gospels are viewing "the first day of Unleavened Bread" not as the 15th of Nisan (the Feast itself), but the 14th of Nisan, which is the OBSERVATION day of the Feast. That is, the synoptic gospels indicate that Jesus OBSERVED the Passover on the 14th of Nisan.
For example, Matthew 26:17 says the following -
Matthew 26:17 (NASB)
17 Now on the first day of Unleavened Bread the disciples came to Jesus and asked, “Where do You want us to prepare for You to eat the Passover?”
Is this this the 15th of Nisan, which is the Feast of Unleavened Bread? No, it is not; it is the early hours of the 14th of Nisan (evening of the preceding day), which is the OBSERVATION day of the Feast of Unleavened Bread. That is, the 14th of Nisan is the "Day of Preparation," which is the day that the Passover Lamb was sacrificed. Why do we know this? Matthew 27:62 says the following -
Matthew 27:62 (NASB)
62 Now on the next day, the day after the preparation, the chief priests and the Pharisees gathered together with Pilate...
The day of preparation is the 14th of Nisan (please see also Mark 14:12; Mark 15:42; and Luke 22:7). Therefore the day AFTER the Day of Preparation is in fact PASSOVER, or the "first day" of the Feast of Unleavened Bread. In other words, the pharisees approached Pilate on the actual Passover Day (15th Nisan), because Jesus was placed in the grave on the eve of Passover (he was buried before Passover started at dusk the previous day, 14th of Nisan).
In summary, there is a slight nuance between the OBSERVATION of the Feast of Unleavened Bread (Ex 12:17-18), which continues for eight days, and the Feast of Unleavened Bread (Lev 23:6), which continues for seven days. This nuance is the cause of the confusion of the PERCEIVED discrepancy of dates between the synoptic gospels and the gospel of Saint John. That is, the synoptics are benchmarking their timing of the "first day" of the OBSERVATION of the Feast based on Ex 12:17-18, and Saint John is benchmarking his timing from the actual FEAST DAY based on Lev 23:6.