Solved! Just got an rca 7"tablet today. The sound only works with headphones. I've checked mute, volume, settings

Solution
Did you check to see its not on in Bluetooth mode? Also try rebooting it and see it that works, if not then try safe mode and see if sound works through the speakers without the headphones
Did you check to see its not on in Bluetooth mode? Also try rebooting it and see it that works, if not then try safe mode and see if sound works through the speakers without the headphones
 
Solution
If it is brand new and giving you problems, you may want to return it and have them give you a working device. No new device should have problems.