$p(t)=t^3+2t^2 - 4t -8=0$

well...

If it can't be factored there is a formula for the roots of a cubic equation but it's quite involved.

If it can be factored by the rational root theorem you know that any factors $(t+a)$ will be such that $a$ divides 8, the constant term of the polynomial.

that limits the values of $a$ to

$\pm 1, \pm 2, \pm 4, \pm 8$

so start trying to divide $p(t)$ by $(t \pm1), (t\pm 2), \dots$

or you could head over to Wolframalpha.com and type

Factor[t^3+2t^2 - 4t -8]

and it will do the grunt work for you.