By splitting the middle term

v² + 4√3 v - 15 = 0

v² + (5√3v - 3√3v) - 15 = 0

v² + 5√3v - 3√3v - 15 = 0

v (v + 5√3) - √3(v + 5√3) = 0

(v + 5√3)(v - √3) = 0

⇒ v = - 5√3, √3

Verification:

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

α + β = - b/a

(- 5√3) + (√3) = - 4√3

= - 4√3 = - 4√3

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

(- 5√3)(√3) = - 15

- 15 = - 15