1. **State the problem:** Expand and simplify the expression $t(7t - 2) + 3t(4t - 5)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$t(7t - 2) = t \times 7t - t \times 2 = 7t^2 - 2t$$ $$3t(4t - 5) = 3t \times 4t - 3t \times 5 = 12t^2 - 15t$$ 3. **Combine the results:** $$7t^2 - 2t + 12t^2 - 15t$$ 4. **Group like terms:** $$ (7t^2 + 12t^2) + (-2t - 15t)$$ 5. **Simplify each group:** $$7t^2 + 12t^2 = 19t^2$$ $$-2t - 15t = -17t$$ 6. **Write the final simplified expression:** $$19t^2 - 17t$$