Look at the text and do not twist it---
Act 15:14 Simeon hath declared how God at the first did visit the Gentiles, to take out of them a people for his name.
Act 15:15 And to this agree the words of the prophets; as it is written,
Act 15:16 After this I will return, and will build again the tabernacle of David, which is fallen down; and I will build again the ruins thereof, and I will set it up:
Act 15:17 That the residue of men might seek after the Lord, and all the Gentiles, upon whom my name is called, saith the Lord, who doeth all these things.
Act 15:18 Known unto God are all his works from the beginning of the world.
Act 15:19 Wherefore my sentence is, that we trouble not them, which from among the Gentiles are turned to God:
The Jews expected the Shekeniah Glory to return to the stone Temple from where He departed from.
Instead He first entered the living Temple of Jesus body, and then in similar pattern to His coming into the House of the Lord in King Solomons time, He entered the living Temple of the 120 on the day of Pentecost.
and the gentiles (the word for nations)began seeking after the Lord.
If you do not believe that, then you do not believe God Himself.
LA
120 who, guided by the Spirit, continued to worship in the Temple at Jerusalem.
You remain clueless, in your laziness, LA.
And the "as it is written" refers to the passage that follows.
And it is a passage about Israel's future restoration.
His point being that if the prophets wrote that the Lord will do a work among the Gentiles after He returns, but is doing a work among them before His return, then that is no problem - He did say He would do a work among them...
Acts 15:18 Known unto God are all his works from the beginning of the world.
This also shows that Peter was not wrong in Acts 10.
Rather, that he was thrown off - because the Lord had not yet returned but was now doing a work among the Gentiles before the Twelve had completed the following...
Matthew 10:5 These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not: 10:6 But go rather to the lost sheep of the house of Israel. 10:7 And as ye go, preach, saying, The kingdom of heaven is at hand. 10:8 Heal the sick, cleanse the lepers, raise the dead, cast out devils: freely ye have received, freely give. 10:9 Provide neither gold, nor silver, nor brass in your purses, 10:10 Nor scrip for your journey, neither two coats, neither shoes, nor yet staves: for the workman is worthy of his meat.
10:16 Behold, I send you forth as sheep in the midst of wolves: be ye therefore wise as serpents, and harmless as doves. 10:17 But beware of men: for they will deliver you up to the councils, and they will scourge you in their synagogues; 10:18 And ye shall be brought before governors and kings for my sake, for a testimony against them and the Gentiles. 10:19 But when they deliver you up, take no thought how or what ye shall speak: for it shall be given you in that same hour what ye shall speak. 10:20 For it is not ye that speak, but the Spirit of your Father which speaketh in you. 10:23 But when they persecute you in this city, flee ye into another: for verily I say unto you, Ye shall not have gone over the cities of Israel, till the Son of man be come.