1. We are asked to factorize the quadratic expression $6t^2 - 7t - 20$. 2. First, multiply the leading coefficient and the constant term: $6 \times (-20) = -120$. 3. Find two numbers that multiply to $-120$ and add to the middle coefficient $-7$. These numbers are $8$ and $-15$ because $8 \times (-15) = -120$ and $8 + (-15) = -7$. 4. Rewrite the middle term $-7t$ using $8t$ and $-15t$: $$6t^2 + 8t - 15t - 20$$ 5. Group the terms: $$(6t^2 + 8t) + (-15t - 20)$$ 6. Factor out the greatest common factors from each group: $$2t(3t + 4) - 5(3t + 4)$$ 7. Notice that $(3t + 4)$ is a common factor, so factor it out: $$(3t + 4)(2t - 5)$$ 8. Thus, the factorization of $6t^2 - 7t - 20$ is $$(3t + 4)(2t - 5)$$.