I'm not stating a solution because I believe the reaction, sans riots, was justified, hence no problem. The protests started, not because of assumption of racism, but because of the police's actions being inappropriate to the event, which eventually lead to charges of racism.
As I mentioned previously, standard procedure is to put the officer involved in the shooting on administrative leave while an investigation takes place. Not starting an investigation, and keeping the involved officer on patrol, are not following standard procedure. Ferguson police did not follow procedure, and when they finally did start following procedure when the nation was watching them, they were not transparent with their investigation, a key to keeping an already unsettled public manageable. Furthermore, their releases during the investigation, at least in the beginning, admitted no wrong doing on the force's response and served mainly to defend their actions by, like I mentioned before, character assassinating Brown. And when all this occurs between a white cop in a white establishment and a black man in a black community, racism is the easiest, and most historically correct, assumption to make.
If there was any problem that needed a solution, it was the incompetence of the police department for their handling of the case. I don't know how they're setup, but they behaved entirely inappropriately to the case and the backlash to their handling. And since I'm unsure of the extent of their problems, my only upfront solution would be an investigation into the establishment to better guide its reformation.