Answer
The solution set is $\left\{5, 7\right\}$.
Work Step by Step
Simplify the left side to obtain:
$x(x)-x(12)=-35
\\x^2-12x=-35$
Add $35$ to both sides of the equation to obtain:
$x^2-12x+35=0$
Factor the trinomial by looking for the factors of $35$ whose sum is equal to the coefficient of the middle term ($-12$).
These factors are $-7$ and $-5$. This means that the factored form of the trinomial is $(x-7)(x-5)$.
Thus,
$x^2-12x+35=0
\\(x-7)(x-5)=0$
Equate each factor to 0; then simplify to obtain:
$x-7=0 \text{ or } x-5=0
\\x=7 \text{ or } x=5$
The solution set is $\left\{5, 7\right\}$.
