If you have the traditional sense of pimples, it is that simple. If you have some other skin condition, then I'll agree it's not that simple.
My skin used to be covered in horrible cysts, with huge red pimples and whiteheads as the "best part" of my skin. Genetics basically screwed me over in the skin department. I almost considered Accutane until I tried 2.5% Benzoyl Peroxide.
Now, my skin is just about flawless, give or take the very faded, barely noticeable marks left behind my acne history. Scars have basically faded. Never thought my skin would be this smooth or even.
The trick is to apply the Benzoyl Peroxide VERY generously. Use it much more than a British woman uses sunblock. To SLATHER it would be an understatement. Those tiny samples at the store where you use "On the spot treatment" do not do your skin justice. You need to find some HUGE package of Benzoyl Peroxide, in order to apply a lot of it.