Moshe was born and died on the same day: the 7th of Adar. He lived to be 120 years old (1393 - 1273 BCE).
Rashi (TB Megillah 13b) explains how we know 7 Adar is the day of Moshe's death. 1. The Jews mourned Moshe for 30 days (Deut. 34:8). 2. After mourning Moshe, three days elapsed before the Jews crossed the Jordan River (Joshua 1:11). 3. The Jews crossed the Jordan on 10 Nissan (Joshua 4:19). Therefore, Moshe died 33 days before 10 Nissan, which is 7 Adar.