Answer
The solution set is $\left\{-7, -3\right\}$.
Work Step by Step
Factor the trinomial by looking for the factors of 21 whose sum is equal to the coefficient of the middle term (10).
These factors are 3 and 7. This means that the factored form of the trinomial is $(x+3)(x+7)$.
Thus,
$x^2+10x+21=0
\\(x+3)(x+7)=0$
Equate each factor to 0 then solve each equation to obtain:
$x+3=0 \text{ or } x+7=0
\\x=-3 \text{ or } x=-7$
The solution set is $\left\{-7, -3\right\}$.
