Step 1: 9*(y^2 + 2y ) = x^2 + 6x + 9 <--- factors out 9 from the left side
9*(y^2 + 2y + 1) - 9 = x^2 + 6x + 9 <--- completes the square
Completing the square:
take half of the coefficient of the linear term, then square that.
The coefficient of the linear term is 2 as highlighted in bold in step 1.
Half of that is one, and one squared is one.
So adding one on the inside of the parenthesis means that, by distributive property,
1x9 = 9 is added to the left side. In order to compensate for that, it is required
to subtract 9 from only the left side.
if you want it multiplied out (standard form)
9 y^2 + 18 y = x^2 + 6x + 9
or Factor as you wish
9 ( y + 1)^2 - 9 = (x + 3)^2