Car shakes when driving on the highway at 70 to 80 mph

Like I said at 70-80 mph my car would shake on the highway. At first, I thought about the possibility of the road. However, my previous car same make and model just different years didn't shake on the highway back to home. Also I bought my car from the dealership and it's been a year only.

my car would:
-Move left to right.
-Steering wheel doesn't move left, right or shake.
-It doesn't drift to another lane (meaning it stays in its lane but constantly move left and right like shaking).

what I've done so far:
-I checked the tire pressure making sure all four wheels have the 32 psi. (With a digital air pump and the tire shop mechanic adjust it)
-Did a tire balance on all four wheels.