In 1870, Italy annexed the Papal State and got its hands on Rome. That was just the last piece of the puzzle.
The US government during reconstruction wanted to rebuild the South, both mentally and literally as many places in the south were destroyed by the war. The US decided to do this by supplying civilians (who requested it) with money to buy materials and for their labor to rebuild parts of the South. Carpetbaggers were northerners who moved to the South during reconstruction in order to take advantage of this policy by going town to town asking for money to rebuild, not rebuilding and just going to the next town. These were not your regular ol' 'business reasons' and instead these people were kinda dirtbags.