I'd say mass government spending. We all know that if we throw money at a problem, then the problem will be solved. Just let the experts in charge figure it out.
Another solution is for everyone to have a gun. That way people would think twice about going and shooting up anywhere. And in that rare occurrence when people do decide to try something stupid like this, then it would be AWESOME!!!
Just FYI, these seem like the two extreme solutions on the table and they're both fairly silly.
That being said, I'm fairly anti-gun control and it seems like everything that could fall through the cracks with this guy did fall through the cracks. For example, with background checks (which actually are a pretty good idea), this guy had nothing on his record. I believe that he had no mental issues, no criminal record, not even medication, his record showed a normal young man. So this solution really can't work 100% of the time. In addition, he bought his weapons legally with no controversy until the incident.
Also, tighter laws on carrying weapons seem like a good idea, but then again people who do crazy things will go through black markets to purchase guns when they're illegal, the same way people got booze in the prohibition days and how people get weed and cocaine today. Making things that are bad for us illegal is a sexy solution but not always an appropriate solution.
This isn't really an easy question to answer, it's trying to predict the black swan, the rare occurrence of something terrible that happens. It's sad, but debate on this may be as useful as debates to stop hurricanes or tornadoes.