Answer
The solutions are 2 and 3.
Work Step by Step
$x^{2}$-5x+6=0
$x^{2}$-2x-3x+6=0
x(x-2)-3(x-2)=0
(x-3)(x-2)=0
x-3=0 or x-2=0
x-3+3=0+3 or x-2+2=0+2
x=3 or x=2
The solutions are 2 and 3.
Check
Let x=2
$x^{2}$-5x+6=0
$2^{2}$ -5*2+6=0
4-10+6=0
-6+6=0
0=0
Let x=3
$x^{2}$-5x+6=0
$3^{2}$ -5(3)+6=0
9-15+6=0
0=0
