By splitting the middle

7y² - 11y/3 - 2/3 = 0

21y² - 11y - 2 = 0

21y² + (3y - 14y) - 2 = 0

21y² + 3y - 14y - 2 = 0

3y (7y + 1) - 2(7y + 1) = 0

(7y + 1)(3y - 2) = 0

⇒ y = - 1/7, 2/3

Verification:

Sum of the zeroes = - (coefficient of x) ÷ coefficient of x²

α + β = - b/a

(- 1/7) + (2/3) = - (- 11)/21

= 11/21 = 11/21

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

(- 1/7)(2/3) =

- 2/21 = - 2/21