How did luther's new doctrine of salvation differ from the catholic church's teachings on salvation

Luther proclaimed salvation as a gift of God's grace, rather than something earned by human efforts.  The Roman Catholic Church spoke of God's grace also, but as an enabling power that helped human beings do the works required for obtaining salvation.  Luther still preached that we should do good works, but said those works were a fruit of being saved rather than a source of salvation.

Further details:

Luther had gone through his own personal struggle as a monk, feeling he was always under the judgment of God.  But then he came to realize, from Romans 1:16-17, that "in the gospel the righteousness of God is revealed" that gives salvation apart from human works.  This personal experience became the focus of his theology -- salvation as the free gift of God that lifts sinners from despair.

1.3x - 2 - (3.3x + 5) = 2x + 1

1.3x - 2 - 3.3x - 5 = 2x + 1

-2x - 7 = 2x + 1

-7 = 4x + 1

-8 = 4x

x = -2

speed =5445/33=165 mpm