Delete all "Promotions" Gmail

1. On the left where your inbox is listed there will be a button that says "More"; select it and then click on "All Mail"
2. In the search box type category:promotions and then click on the search magnifier box.
3. Click on the check box to select everything you see on the page. Once you do this you should see an alert that says "Select all conversations that match this search". Click on that to select everything in the category you searched for.
4. Hit delete