Answer
The solution set is $\left\{-8, 7\right\}$.
Work Step by Step
Factor the trinomial by looking for the factors of $-56$ whose sum is equal to the coefficient of the middle term ($1$).
These factors are $-7$ and $8$. This means that the factored form of the trinomial is $(t-7)(t+8)$.
Thus,
$t^2+t-56=0
\\(t-7)(t+8)=0$
Equate each factor to 0; then, solve each equation to obtain:
$t-7=0 \text{ or } t+8=0
\\t=7 \text{ or } t=-8$
The solution set is $\left\{-8, 7\right\}$.
