factorise the left hand side of the equation xxx+7xx-21x-27=0 and the roots are
simplified to
x^3 + 7x^2 - 21x - 27 = 0
try: x = ±1, ±3, ±7
on the second try, I got x=-1 to work
so (x+1) is a factor
by synthetic division I found
x^3 + 7x^2 - 21x - 27 = (x+1)(x^2 + 6x - 27) = 0
(x+1)(x+9)(x-3) = 0
x = -1, -9, and 3