How to Balance?

I was wondering when you create a champion, how you make him or her balanced. For example, is the AP always approximately the same for every champion? For example, Zed. Why didn't you make his q and e less powerful than a normal skill shot so that his shadow and two q's do the same damage as one skillshot? To me that would make his damage balanced compared to Lux or Ezreal. I know a lot of work goes into every champion, and it takes a long time to actually balance a champion, but how does Riot do it? Its quite interesting. Especially with every champion being different, it seems difficult to make most of them equal. My questions are, "What is the process in ensuring a champion is balanced without being boring? What do you change to make him or her balanced (e.g. AP/AD/Movement Speed/AS/Cooldowns/etc.)?"
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