Let #f(x)=(x+6)(x+8)#

Build a sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaaa)##-8##color(white)(aaaaaaa)##-6##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##x+8##color(white)(aaaaa)##-##color(white)(aaaa)##0##color(white)(aaaa)##+##color(white)(aaaaa)##+#

#color(white)(aaaa)##x+6##color(white)(aaaaa)##-##color(white)(aaaa)####color(white)(aaaaa)##-##color(white)(aa)##0##color(white)(aa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaaa)##0##color(white)(aaaa)##-##color(white)(aa)##0##color(white)(aa)##+#

Therefore,

#f(x)>=0# when # x in (-oo,-8] uu [-6, +oo)#

graph{(x+6)(x+8) [-11.54, 0.947, -2.155, 4.09]}