Jesus said
Whoever believes and is baptized will be saved
Sounds simple to me. Do you have an alternative explanation?
Yes! Peter is the apostle to the Jews. His ministry in the NT was not longer than about 12 years. He is not mentioned again after Acts 15 when the apostle Paul took center stage as he went to the gentiles with the gospel of Jesus Christ.
This is the condition for the Jews to receive the Holy Ghost, who was given from heaven on the feast day of Pentecost, Receiving the Holy Ghost is a synonym of being saved. Here is what he told them:
Ac 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
This is a strictly Jewish context, and if you read it, it will prove itself.
This was true also of the Samaritans in Acts 8. It took apostolic authority for them to receive the Holy Ghost, though they were already baptized.
Ac 8:5 Then Philip went down to the city of Samaria, and preached Christ unto them.
Ac 8:12 But
when they believed Philip preaching the things concerning the kingdom of God, and the name of Jesus Christ, they were baptized, both men and women.
BUT THEY WERE NOT SAVED
YET
Ac 8:14 Now when the apostles which were at Jerusalem heard that Samaria had received the word of God, they sent unto them Peter and John: (both of them were apostles)
15 Who, when they were come down,
prayed for them, that they might receive the Holy Ghost:
16 (For as yet he was fallen upon none of them:
only they were baptized in the name of the Lord Jesus.)
17
Then laid they their hands on them, and they received the Holy Ghost.
Did you get that? Baptism did not save these people.
Here is why the apostle had to confirm their faith:
Joh 20:21 Then said Jesus to them (thje 11 apostles) again, Peace [be] unto you: as [my] Father hath sent me, even so send I you. (With his same authority)
21 Then said Jesus to them again, Peace be unto you: as my Father hath sent me, even so send I you.
22 And when he had said this, he breathed on them, and saith unto them, Receive ye the Holy Ghost:
23 Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained.
If you did not get that, you should read it again.
It was the apostles ministry to say whether the Samaritans would receive forgiveness of sins and the Holy Ghost. Peter retained the sins of Simon!!
But look at Acts 10 when the gospel went to gentiles for the first time.
Ac 10:43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
45 And they of the circumcision which believed were astonished, as many as came with Peter,
because that on the Gentiles also was poured out the gift of the Holy Ghost.
46 For they heard them speak with tongues, and magnify God. Then answered Peter,
47 Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we?
48
And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
Now,there can be no doubt that gentiles received the Holy Ghost when they believed and before they were baptized. They were then told to be baptized but not so they could be more saved.
In case anyone were to doubt they were saved by receiving the holy Ghost, we have this explanation by Peter to the Jerusalem church.
13 And he shewed us how he had seen an angel in his house, which stood and said unto him, Send men to Joppa, and call for Simon, whose surname is Peter;
14
Who shall tell thee words, whereby thou and all thy house shall be saved.
15 And as I began to speak, the Holy Ghost fell on them, as on us at the beginning.
16 Then remembered I the word of the Lord, how that he said, John indeed baptized with water; but ye shall be baptized with the Holy Ghost.
17 Forasmuch then as God gave them the like gift as he did unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God?
18 When they heard these things, they held their peace, and glorified God, saying, Then hath God also to the Gentiles granted repentance unto life.
The Holy Ghost falling on them when they believed was salvation to them, according to Peter.
The gentiles never were required to repent and be baptized in Jesus name for the remission of sins to receive the Holy Ghost. However, the Jews did during the entire apostolic age while Israel had a national identity.
7 But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as the gospel of the circumcision was unto Peter;
8 (For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles

9 And when James, Cephas, and John, who seemed to be pillars, perceived the grace that was given unto me, they gave to me and Barnabas the right hands of fellowship; that we should go unto the heathen, and they unto the circumcision.
10 Only they would that we should remember the poor; the same which I also was forward to do.