3t^2-5t+6 + -8t^2+7t-9

To add these two expressions together:

3t^2 - 5t + 6 + -8t^2 + 7t - 9

First, combine like terms:

(3t^2 - 8t^2) + (-5t + 7t) + (6 - 9)

=-5t^2 + 2t - 3

So, the simplified expression is -5t^2 + 2t - 3.