Question

Consider the polynomial equation x(x-3)(x+6)(x-7)=0. What are the zeros of the equation?

Answer 1

anything times zero is equal to zero
hence for,

x(x-3)(x+6)(x-7)=0

only one of the groups/parenthesis must be equal to zero
therefore
x=0
x-3=0
x+6=0
x-7=0

just solve for all the x's, all those values are considered zeros of the equation

Answer 2

hello :
x(x-3)(x+6)(x-7)=0
x=0 or x-3=0 or x+6=0 or x-7=0
x=0 or x=3 or x=-6 or x=7
the zeros of the equation : 0 , 3 , -6 , 7