By splitting the middle term

5t² + 12t + 7 = 0

5t² + (5t + 7t) + 7 = 0

5t² + 5t + 7t + 7 = 0

5t (t + 1) + 7(t + 1) = 0

(t + 1)(5t + 7) = 0

(t + 1)(5t + 7) = 0

⇒ t = - 1. - 7/5

Verification:

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

α + β = - b/a

(- 1) + (- 7/5) = - (12)/5

= - 12/5 = - 12/5

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

(- 1)(- 7/5) = - 7/5

- 7/5 = - 7/5