Question: User: -3(t+5)=2(t-5)
1. **State the problem:** Solve the equation $$-3(t+5)=2(t-5)$$ for the variable $$t$$.
2. **Apply the distributive property:** Multiply $$-3$$ by each term inside the parentheses on the left side, and multiply $$2$$ by each term inside the parentheses on the right side.
$$-3 \times t + (-3) \times 5 = 2 \times t + 2 \times (-5)$$
which simplifies to
$$-3t - 15 = 2t - 10$$
3. **Collect like terms:** Add $$3t$$ to both sides to get all $$t$$ terms on one side.
$$-3t - 15 + 3t = 2t - 10 + 3t$$
which simplifies to
$$-15 = 5t - 10$$
4. **Isolate the term with $$t$$:** Add $$10$$ to both sides.
$$-15 + 10 = 5t - 10 + 10$$
which simplifies to
$$-5 = 5t$$
5. **Solve for $$t$$:** Divide both sides by $$5$$.
$$\frac{-5}{\cancel{5}} = \frac{5t}{\cancel{5}}$$
which simplifies to
$$-1 = t$$
6. **Final answer:** $$t = -1$$