Answers: x = 2 or x = 3
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Step-by-step explanation:
Use the zero product property. This is the idea where if A*B = 0, then either A = 0 or B = 0.
This works because 0 times any number is always 0.
In this case A = x-2 and B = x-3
So,
(x-2)(x-3) = 0
x-2 = 0 or x-3 = 0
x = 2 or x = 3
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If we plugged x = 2 back into the original equation, we get
(x-2)(x-3) = 0
(2-2)(2-3) = 0
(0)(-1) = 0
0 = 0
Which confirms x = 2
Let's do the same for x = 3
(x-2)(x-3) = 0
(3-2)(3-3) = 0
(1)(0) = 0
0 = 0
So x = 3 is confirmed as well.