The private pilot, who was not a flight instructor, allowed the student pilot to fly the airplane from the left front seat, after the student pilot purchased the airplane. The student pilot and the private pilot departed and landed at an intermediate airport. They returned to the airplane, conducted a thorough preflight inspection and departed to their destination airport. While landing at the destination airport, the student pilot applied uneven brakes and the airplane veered to the left, striking the runway lights. The private pilot also applied brakes and informed the student pilot to "power back." The student pilot then added full power, the airplane departed the left side of the runway, and collided with a tree. The airplane sustained structural damage to the left wing. The private pilot stated there were no mechanical problems with the airplane prior to the accident.