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

leads to

either (3x - 4) = 0 or (5x + 2) = 0.

Solve these two equations for x and this will give you the two values of x that give (3x - 4)(5x + 2) = 0.

Penny