Let
#f(x)=(x-4)(x+3)(2-x)#
We build a sign chart
#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-3##color(white)(aaaa)##2##color(white)(aaaaa)##4##color(white)(aaaaa)##+oo#
#color(white)(aaaa)##x+3##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##2-x##color(white)(aaaaa)##+##color(white)(aaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##-#
#color(white)(aaaa)##x-4##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##-#
Therefore,
#f(x)<=0# when #x in [-3,2] uu [4,+oo)#