There's several solutions but most of those are impossible to implement in today's world with its token efforts and sensibilities. There's no hope of educating the extremism out as long as the places where extremism thrives, lacks the infrastructure to have a real education system and the ability to protect infrastructure. It would still require a large military presence and a lot of time for it to work. The UN and the middle eastern nations are unwilling to commit that kind of resources for this kind of solution.
The other way is through war (unconventional) and basically wiping out any islamic extremists elements within any nation. Some might say we're already doing this but we're not. It would take a very large military presence in the middle east to track down and eliminate all elements. Because extremists don't wear uniforms or follow any law regarding war, the militaries hunting them would have to fight fire with fire in some sense. Who they can treat as combatants and how they could treat would change. Of course, the UN and most governments are unwilling to go with this option
Islam is becoming more unpopular and there's this sort of anti-islamic mindset that's growing by the day due to the consistent terrorist attacks. Eventually, that would empower a future leader with extreme views on islam or political group/party with extreme views and enable them to gain control of governments. Most likely, this group would go with option 2 but it would be a lot worse for everyone is every sense.
My point is that people and the nations they live in need to commit to a course of action and stick with it for good or bad. If they don't, something far worse will eventually happen because of their inaction.
