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 2:34

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.