The solution set of $x^2+6x+9=0$  is

$x^2+2\left(x\right)\left(3\right)+3^2=0$

${\left(x+3\right)}^2=0$

$\left(x+3\right)\left(x+3\right)=0$

$x=-3,-3$

Solution set $=\left\{-3,-3\right\}=\left\{-3\right\}$

In set, repeated element are written only once.