Answer
$\color{blue}{x = \left\{-3, 10\right\}}$
Work Step by Step
Since the leading coefficient is $1$, the trinomial can be factored by looking for the factors $c$ and $d$ of the constant term $-30$ whose sum is equal to the middle term's coefficient ($c+d=-7$).
The factored form of the trinomial then is $(x+c)(x+d)$
Note that:
$-10(3)=-30$ and $-10+3=-7$
Thus, the factors of $-30$ that we are looking for are $-10$ and $3$.
This means that the factored form of the trinomial is:
$=(x+(-10))(x+3)
\\=(x-10(x+3)$
Therefore the equation becomes:
$(x-10)(x+3)=0$
Use the Zero-Product Property (which states that if $xy=0$, then either $x=0$ or $y=0$ or both are zero) by equating each factor to zero to obtain:
$x-10=0 \text{ or } x+3=0$
Solve each equation to obtain:
$x=10$ or $x=-3$
Therefore, the solutions to the given equation are:
$\color{blue}{x = \left\{-3, 10\right\}}$