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So if you subtract the 0 out from the left side, the equation is now 
. Since a x is common in both of the terms on the left side, you can factor it out, now making the equation look like 
. When factoring, each of the separate things (x and (x-3)), must equal zero while the other one doesn't matter. So in order for the equation to be 0, the only potential options for x is 0 and 3. Therefore x=0 and x=3 are the two solutions