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)

X=-3y

3y^2=3*3=9y

12y+9y=21y-3y=18y