Bitcoin mining solving equations, what it actually is?

[manselr]

It probably doesn't get any better than this in trying to explain what's going on in bitcoin's mining:

https://www.youtube.com/watch?v=y3dqhixzGVo

So now you know what to do if you want to do it manually.

This is a great insight into how much stress the mining machines go through. Imagine having to do that millions of time daily. That shows how secure the network is against attackers.