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 Question from Millie, a student: (3x-4)(5xplus2)=0

Millie,

One of the important facts about our number system is that if you multiply two non-zero numbers the result is not zero. Hence if you multiply the two numbers (3x - 4) and (5x + 2) and obtain an answer of zero then either (3x - 4) is zero or (5x + 2) is zero. Hence the equation

(3x - 4)(5x + 2) = 0