Z^2 -6z+9=0 Factor and solve

Factor because if we have
yz=0 then we can assume y and/or z=0

so factor
so the easiest way is to find what 2 numbers add to -6 and multiply to get 9 so
we know that they must be both - because we must have x+x=(-) and x^2=+ so therefor they must be negative
factors of 9=3 and 3 so
-3 and -3
-3+-3=-6 perfect

(z-3)(z-3)=0

set each to zero
z-3=0
add 3
z=3

z=3 is the answer