Answer
The solution set is $\left\{2, 14\right\}$.
Work Step by Step
Factor the trinomial by looking for the factors of $28$ whose sum is equal to the coefficient of the middle term ($-16$).
These factors are $-14$ and $-2$. This means that the factored form of the trinomial is $(x-14)(x-2)$.
Thus,
$x^2-16x+28=0
\\(x-14)(x-2)=0$
Equate each factor to 0; then, solve each equation to obtain:
$x-14=0 \text{ or } x-2=0
\\x=14 \text{ or } x=2$
The solution set is $\left\{2, 14\right\}$.
