1 Kings 2:25

2:25 King Solomon then sent Benaiah son of Jehoiada, and he killed Adonijah.

1 Kings 2:29-34

2:29 When King Solomon heard that Joab had run to the tent of the Lord and was right there beside the altar, he ordered Benaiah son of Jehoiada, “Go, strike him down.” 2:30 When Benaiah arrived at the tent of the Lord, he said to him, “The king says, ‘Come out!’” But he replied, “No, I will die here!” So Benaiah sent word to the king and reported Joab’s reply. 2:31 The king told him, “Do as he said! Strike him down and bury him. Take away from me and from my father’s family the guilt of Joab’s murderous, bloody deeds. 2:32 May the Lord punish him for the blood he shed; behind my father David’s back he struck down and murdered with the sword two men who were more innocent and morally upright than he – Abner son of Ner, commander of Israel’s army, and Amasa son of Jether, commander of Judah’s army. 2:33 May Joab and his descendants be perpetually guilty of their shed blood, but may the Lord give perpetual peace to David, his descendants, his family, and his dynasty.” 2:34 So Benaiah son of Jehoiada went up and executed Joab; he was buried at his home in the wilderness.

1 Kings 2:46

2:46 The king then gave the order to Benaiah son of Jehoiada who went and executed Shimei.

So Solomon took firm control of the kingdom.