(x+3)²=17x+21
expand first
x²+6x+9=17x+21
minus 17x+21 both sides
x²-11x-12=0
we can easily factor
what 2 numbers multiply to get -12 and addd to get -11?
-12 and 1
(x-12)(x+1)=0
x-12=0
x=12
x+1=0
x=-1
x=-1 and 12
you can use either method, I would use factoring