Answer
$$4t^2-3t+6$$
Work Step by Step
In order to divide monomials, we look for common terms in the numerator and the denominator that can be canceled out. Doing this, we find:
$$\frac{20t^3-15t^2+30t}{5t} \\ \frac{5t\left(4t^2-3t+6\right)}{5t} \\ 4t^2-3t+6$$
Note, if we wanted to check this answer, we could multiply the answer by the value we canceled out to see if that matched the original numerator.