A deshedding comb/brush will work much better than a standard brush. There is one particular brand that has impressed us and our clients. Look up Zoom Groom by Kong, on Amazon. Our clients kept bugging us to sell the Zoom Groom to them. The Amazon price is better than what we sell them for, but we are mobile and have the product on our trucks and provide the convenience of the groomers being able to have product anytime we are near their shops. The clients were willing to pay a little more for that convenience.
I always check Amazon first when I am going to order something. There are many reviews on there, on the Zoom Groom, and many other products.
Dog hair sheds and there is no way to eliminate it. We have had Bouvier Des Flanders and while they don't leave hair behind, what does shed is trapped in their coat and they have to be brushed and groomed often. Brushing often, with a good brush, is the best bet. Some of our dogs used to let us use a shop vac on them. I don't know if there are any drawbacks to that or if it will help much, but they thought it was fun.
Have you tried to use a yard blower to chase the hair out of the garage?