Answer
$\left\{3, 5\right\}$
Work Step by Step
Move all terms to the left side. Note that when a term moves to the other side of the equation, the sign changes to its opposite.
$x^2-8x+15=0$
With a leading coefficient of $1$, factor the trinomial by looking for factors of the constant term $(15)$ whose sum is equal to the coefficient of the middle term $(-8)$.
Note that $15=(-5)(-3)$ and $-5+(-3) = -8$.
This means that the factors of the trinomial are $x-5$ and $x-3$.
Thus, the factored form of the trinomial is:
$(x-5)(x-3)=0$
Equate each factor to zero then solve each equation to obtain:
$x-5 = 0 \text{ o } x-3=0
\\x=5 \text{ or } x=3$
The solution set of the given equation is $\left\{3, 5\right\}$.
