Final answer:
To solve the equation by completing the square, rearrange the terms and isolate y. Complete the square by adding and subtracting the square of half the coefficient of y. Divide both sides by 3 to solve for y.
Step-by-step explanation:
To solve the equation by completing the square, let's first rearrange the terms:
3y(y-2) = 4-2y
We want to get the equation in the form of (y - c)^2 = d. To do this, we can expand the left side, isolate the y terms, and complete the square:
3y^2 - 6y = 4 - 2y
3y^2 - 4y + 4 = 0
Now, let's complete the square by adding and subtracting the square of half the coefficient of y:
3(y^2 - 4y + 4/3) = 0
3(y - 2/3)^2 = 0
Finally, divide both sides by 3 to solve for y:
(y - 2/3)^2 = 0
y - 2/3 = 0
y = 2/3