No, those 30 seconds lightly brushing with some toothpaste and a quick rinse with your mouthwash does not count as a complete brushing. In fact, millions of Americans do not do a proper job when they brush, even if they brush twice a day.
Fort Collins dentists recommend trying to be as thorough as possible. When you brush, make sure that every side and angle of every single tooth receives at least a couple of strokes. This includes the backs of the teeth, along where the tongue sits, and along the roof of your mouth. It is also good to get close to the gum line and brush your tongue itself. This will keep your breath fresher longer and give you stronger, more durable teeth.