Two methods by which white americans attempted to solve the "indian problem" and acquire tribal land were:

The first way they tried to solve the problem was assimilation.

This means that the US tried to change the culture of Native Americans and in essence this was a cultural transformation. They wanted the Native Americans to live by the rules and norms of the European culture. This was primarily attempted through education.

The second solution was even worse and it was removal.

The US government "relocated" the Native American tribes to different parts of the country while they continued to settle and grow as a country. Many Native American tribes resisted which led to many armed conflicts.