3x^2+3x+2y=0 complete the square and reduce to one standard form y-b=A (x-a) ^2 or x-a=A (y-b) ^2

We are asked to transform the equation 3x^2+3x+2y=0 into the standard form by applying the technique of completing the square.

3 (x^2+x + 1/4) = - 2y + 3/4

3 (x + 1/2) ^2 = - 2 (y - 3/8)

-3/2 (x + 1/2) ^2 = (y - 3/8)

this follows the standard from y-b=A (x-a) ^2