Answer
The solution set is $\left\{-2, 5\right\}$.
Work Step by Step
Factor the trinomial by looking for the factors of $-10$ whose sum is equal to the coefficient of the middle term ($-3$).
These factors are $-5$ and $2$. This means that the factored form of the trinomial is $(x-5)(x+2)$.
Thus,
$x^2-3x-10=0
\\(x-5)(x+2)=0$
Equate each factor to 0 then solve each equation to obtain:
$x-5=0 \text{ or } x+2=0
\\x=5 \text{ or } x=-2$
The solution set is $\left\{-2, 5\right\}$.
