1. State the problem: We want to find the product of the expressions $(-8x + 7)$ and $(6x - 5)$. 2. Use the distributive property (FOIL method) to multiply: $$(-8x + 7)(6x - 5) = (-8x)(6x) + (-8x)(-5) + 7(6x) + 7(-5)$$ 3. Calculate each term: $$(-8x)(6x) = -48x^2$$ $$(-8x)(-5) = 40x$$ $$7(6x) = 42x$$ $$7(-5) = -35$$ 4. Combine all terms: $$-48x^2 + 40x + 42x - 35$$ 5. Simplify by combining like terms ($40x + 42x$): $$-48x^2 + 82x - 35$$ 6. Final answer: $$oxed{-48x^2 + 82x - 35}$$