x cannot = 0
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The values of x that give zero besides x=0 are x = -4 and x=2. Why? The "zero factor property" tells us that:
a*b=0 if either a=0 or b=0.
In this case we have 3 factors: x, (x+4) and (x-2), so x(x+4)(x-2) = 0 if any of the factors is zero
(x+4) = 0 when x = -4
(x-2) = 0 when x = 2