1. **State the problem:** Simplify the expression $$\frac{6p^2 - 15p}{25 - 4p^2}$$. 2. **Factor numerator and denominator:** - Numerator: $$6p^2 - 15p = 3p(2p - 5)$$ - Denominator: $$25 - 4p^2$$ is a difference of squares, so $$25 - 4p^2 = (5 - 2p)(5 + 2p)$$. 3. **Rewrite the fraction:** $$\frac{3p(2p - 5)}{(5 - 2p)(5 + 2p)}$$ 4. **Notice that $$2p - 5$$ and $$5 - 2p$$ are negatives of each other:** $$2p - 5 = -(5 - 2p)$$ 5. **Replace $$2p - 5$$ with $$-(5 - 2p)$$:** $$\frac{3p \cancel{(2p - 5)}}{\cancel{(5 - 2p)}(5 + 2p)} = \frac{3p(- (5 - 2p))}{(5 - 2p)(5 + 2p)}$$ 6. **Cancel the common factor $$(5 - 2p)$$:** $$\frac{3p \cancel{-(5 - 2p)}}{\cancel{(5 - 2p)}(5 + 2p)} = \frac{-3p}{5 + 2p}$$ 7. **Final simplified expression:** $$\boxed{\frac{-3p}{5 + 2p}}$$