#### Answer

$x=\{ 2, 3 \}$

#### Work Step by Step

The two numbers whose product is $ac=1(6)=6
$ and whose sum is $b=
-5
$ are $\{
-2,-3
\}$. Using these two numbers to decompose the middle term of the given equation, $
x^2-5x+6=0
,$ results to
\begin{array}{l}\require{cancel}
x^2-2x-3x+6=0
\\\\
(x^2-2x)-(3x-6)=0
\\\\
x(x-2)-3(x-2)=0
\\\\
(x-2)(x-3)=0
.\end{array}
Equating each factor to zero (or the Zero-Factor Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
x-2=0
\\\\
x=2
,\\\\\text{OR}\\\\
x-3=0
\\\\
x=3
.\end{array}
Hence, the solutions are $
x=\{ 2, 3 \}
.$