Answer
Solution set:$\{3,9\}$
Work Step by Step
$x^{2} -12x+27 = 0$
$x^{2} -12x =-27$
By adding the square of half the co-efficient of $x$ to both sides, we get,
$x^{2} -12x+36 =-27+36$
$x^{2} -12x+36 =9$
By factoring,
$(x-6)^{2}=9$
$(x-6)=±\sqrt 9$
$(x-6)=±3$
$x=6±3$
$x=6+3$ or $x=6-3$
$x=9$ or $x=3$
Solution set:$\{3,9\}$