There are a number of things you can do to speed up combat, or any other dice rolling action for that matter, the most common way is to roll your dice ahead of your turn. I know a number of players that do this and it’s great as long as your GM will allow it.
But what do you do if you have multiple actions that all resolve on your turn? Grab an extra set (or two, or three) and use different colors to represent the different actions.
By using a different color of die for each action you can roll them all at once and there will no confusion as to which result roll (damage) goes with which action roll (attack).