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x(x+4)(x-2)=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=0
 
(x+4) = 0 when x = -4
 
(x-2) = 0 when x = 2