How did Martin Luther solve the problems of the catholic church

Answer: to showed them how people were saved by faith alone instead of indulgences

Explanation:

Luther believed people were saved by faith alone and that this was the summary of all Christian doctrine, and that the Catholic Church of his day had got this wrong.

It's often stated Catholics, by contrast to Protestants, believe a mixture of faith and works is necessary for salvation.

It should be noted, however, many Catholics believe their objection to "faith alone" has been misunderstood. They would say true faith can't actually be separated from works, and that Catholics agree it is grace that gives salvation. "Neither the Church nor the pope can establish articles of faith. These must come from Scripture," he said.

then eventually

Protestants and Catholics have been able to find common ground on this issue in recent years. In 1999, Lutherans and Catholics officially reached a consensus on much of their beliefs about salvation.