As we are given with an equation as follows :
[tex]{:\implies \quad \sf x^{2}(x+2)(x+6)=0}[/tex]
As product of these three factors is equal . So , any of these factor can be 0 as product is 0 only when one of the expressions which are multiplied is 0. So , 3 cases arises as follows ;
Case I :-
[tex]{:\implies \quad \sf x^{2}=0}[/tex]
On raising ½ power to both sides we have ;
[tex]{:\implies \quad \sf x=\pm \: 0}[/tex]
Now , as +0 and -0 have no difference in them . So , it's simply 0
[tex]{:\implies \quad \sf So\quad x=0}[/tex]
Case II :-
[tex]{:\implies \quad \sf x+2=0}[/tex]
[tex]{:\implies \quad \sf So\quad x=-2}[/tex]
Case III :-
[tex]{:\implies \quad \sf x+6=0}[/tex]
[tex]{:\implies \quad \sf So\quad x=-6}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{Hence \:\: x\in \{0,\: -6,\: -2\}}}}[/tex]
