Answer
The solution set is $\left\{3, 15\right\}$.
Work Step by Step
Factor the trinomial by looking for the factors of $45$ whose sum is equal to the coefficient of the middle term ($-18$).
These factors are $-15$ and $-3$. This means that the factored form of the trinomial is $(x-15)(x-3)$.
Thus,
$x^2-18x+45=0
\\(x-15)(x-3)=0$
Equate each factor to 0; then, solve each equation to obtain:
$x-15=0 \text{ or } x-3=0
\\x=15 \text{ or } x=3$
The solution set is $\left\{3, 15\right\}$.
