#### Answer

The solution set is $\left\{-9, 8\right\}$.

#### Work Step by Step

Factor the trinomial by looking for the factors of $-72$ whose sum is equal to the coefficient of the middle term ($1$).
These factors are $-8$ and $9$. This means that the factored form of the trinomial is $(t-8)(t+9)$.
Thus,
$t^2+t-72=0
\\(t-8)(t+9)=0$
Equate each factor to 0; then, solve each equation to obtain:
$t-8=0 \text{ or } t+9=0
\\t=8 \text{ or } t=-9$
The solution set is $\left\{-9, 8\right\}$.