Question 467357
The critical numbers are -6, 0, 8.

In the interval ({{{-infinity}}}, -6): {{{x(x + 6)(8-x)>0}}}.  (Use the test number x = -7.)

In the interval (-6, 0): {{{x(x + 6)(8-x)<0}}}.  (Use the test number x = -5.)

In the interval (0, 8): {{{x(x + 6)(8-x)>0}}}.  (Use the test number x = 1.)

In the interval (8, {{{infinity}}}): {{{x(x + 6)(8-x)<0}}}.  (Use the test number x = 9.)

The critical numbers themselves -6,0, and 8 satisfy the inequality.  Hence the solution set is 

({{{-infinity}}}, -6]U [0, 8].