From the book of Acts we know Paul wrote Romans after a long and bitter controversies in both Galatia and Corinth. As a result of these conflicts, Romans “constitutes a ‘manifesto’ setting forth his deepest convictions on central issues” (Kruse, Romans, 9). This manifesto was written and published to gain the widest publicity. It is possible the core of the letter was sent to other Pauline churches, although there is no manuscript evidence for this.
Paul also wrote Romans just prior to his trip to Jerusalem to deliver the collection to the poor saints in Jerusalem. The book of Romans may have been intended to gain the favor of the Roman church as he approached the contentious Jerusalem church. Romans 15:30-33 specifically asks the Roman church to pray for Paul because he is not sure what reception he will receive when he arrives in Jerusalem.
Whatever the case, Paul assumes Roman church had close ties with Jerusalem and some communication regularly occurred between these two communities. Paul may have though the Roman church had some level of influence on Jerusalem leaders like James, the brother of Jesus. In fact. At least one scholar suggested the real target audience of the letter is the Jerusalem church. Paul wants the letter to get to the potentially hostile Jerusalem church to make clear his theology in order to diffuse any suspicion.
With this in mind, Paul wrote Romans gain the cooperation of the Roman church for his mission to Spain. He needed the assistance of the Roman Christians to provide contacts in Spain because of the lack of Jewish population there that could provide him with a base of operations. Paul faced an unusual problem in Spain, Greek was commonly spoken. He may have needed local help from Romans to assist him in Latin. Romans would then be a kind of discipleship letter which ensured the Roman churches were equipped with his Gospel and were not exported a Roman system of pursuit of honor to “barbarian Spain.” Paul argues in Romans that God saves all sinners impartially regardless of culture through Jesus Christ.
As F. F. Bruce pointed out in The Romans Debate, any combination of the suggestions made over my last several posts may be in the background of Romans. Paul had several motivations to write a complex book like Romans, in contrast to a letter like Galatians which is targeted at a single issue, or 1 Corinthians which deals with serious problems in the church and answers several questions.