What an algebra equation is. I could solve linear equations, quadratic equations, and systems of equations by adding/subtracting/multiplying/dividing both sides of the equation and by adding two equations together. But I didn't know why you were allowed to do any of those things, or what else might be allowed. Are you allowed to square both sides? Raise both sides to a power?

It wasn't until maybe my third year of algebra that I realized an equation means both sides of the equation are equal to each other, which means you can perform any operation at all to both sides, and the result will still be equal.