How to put x+3y^2+12y=18 into vertex form step by step

That is
x=(y-h)^2+k where vertex is (k,h)

so

just like normal except that you do it with y

minus (3y^2+12y) from both sides
x=-3y^2-12y+18
complete the square
x=-3(y^2+4y)+18
x=-3(y^2+4y+4-4)+18
x=-3((y+2)^2-4)+18
x=-3(y+2)^2+12+18
x=-3(y+2)^2+30

that is it

x=-3(y+2)²+30
vertex is (30,-2)

Same length is comparing because it’s saying its the same and not different