King Jeroboam did many other things. He fought wars and continued to rule the people. All the things he did are written in the book The History of the Kings of Israel.
Hoshea son of Elah made plans against Pekah son of Remaliah. Hoshea killed Pekah. Then Hoshea became the new king after Pekah. This was during the 20th year that Jotham son of Uzziah {was king of Judah}.