When driving between sixty to eighty MPH car shakes

Harry here. A car with only 87,000 miles probably doesn't have any serious suspension problems that would cause this. If you feel the shaking mainly in your seat, that means the problem is in the rear of the car. If you feel it in the steering wheel, it means that the problem is in the front end. Takes your car to a tire shop and get the appropriate wheels balanced. If in doubt, get all four of them done.

Cars have balancing weights on the wheels. The weights are installed and adjusted when the tire is changed. Sometimes the weights can fall off for whatever reasons, causing the wheels to shake and vibrate at higher speeds.

Here's a descriptive wiki on it: https://en.m.wikipedia.org/wiki/Tire_balance

Try that and see what you find. Also have a trusted mechanic check the tires themselves (not the tire shop people, because they may say whatever they need to make a sale).

Here's our info on inspecting the tires if you want to do it yourself: https://www.2carpros.com/articles/how-car-tires-work

Let me know what you find and we'll go from there

See that’s where I’m confused. I just had brand new tires and rims put on the car that was followed by a weight and balance on them as well. Not sure if it just needs an alignment now because, I have yet to get that done.

If it's an alignment issue you might be able to tell based on tire wear. It could be that when they balanced them, one of the weights was left a little loose and it came off. I'd still have them rebalanced.