Technically, we're allowed to do anything to an equation as long as we do it to both sides of an equation. This includes dividing: we could divide by a number (or constant) or even divide by a variable, BUT... in dividing by a variable, though it is technically mathematically correct, we would lose a solution to a quadratic equation. As shown here, the best method is always to set the equation equal to zero, factor, and then solve using the zero product property rather than divide by a variable.
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