#### Answer

The solution set is $\left\{3, 6\right\}$.

#### Work Step by Step

Factor the trinomial by looking for the factors of 18 whose sum is equal to the coefficient of the middle term (-9).
These factors are $-6$ and $-3$. This means that the factored form of the trinomial is $(x-6)(x-3)$.
Thus,
$x^2-9x-18=0
\\(x-6)(x-3)=0$
Equate each factor to 0 then solve each equation to obtain:
$x-6=0 \text{ or } x-3=0
\\x=6 \text{ or } x=3$
The solution set is $\left\{3, 6\right\}$.