1 Kings 2:24-25

2:24 Now, as certainly as the Lord lives (he who made me secure, allowed me to sit on my father David’s throne, and established a dynasty for me as he promised), Adonijah will be executed today!” 2:25 King Solomon then sent Benaiah son of Jehoiada, and he killed Adonijah.

1 Kings 2:31

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.

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.