1. **State the problem:** Solve the equation $-7(8b-2)=32+3b$ for $b$. 2. **Apply the distributive property:** Multiply $-7$ by each term inside the parentheses: $$-7 \times 8b = -56b$$ $$-7 \times (-2) = +14$$ So the equation becomes: $$-56b + 14 = 32 + 3b$$ 3. **Group like terms:** Move all terms involving $b$ to one side and constants to the other: Add $56b$ to both sides: $$14 = 32 + 3b + 56b$$ Simplify the right side: $$14 = 32 + 59b$$ 4. **Isolate the variable term:** Subtract $32$ from both sides: $$14 - 32 = 59b$$ $$-18 = 59b$$ 5. **Solve for $b$:** Divide both sides by $59$: $$b = \frac{-18}{59}$$ **Final answer:** $$b = -\frac{18}{59}$$