1. **State the problem:** Solve the equation $$4b^2 = 7b$$ for $b$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$4b^2 - 7b = 0$$ 3. **Factor the equation:** Factor out the common factor $b$: $$b(4b - 7) = 0$$ 4. **Apply the zero product property:** For the product to be zero, either factor must be zero: - $b = 0$ - $4b - 7 = 0$ 5. **Solve each equation:** - $b = 0$ - $4b - 7 = 0 \Rightarrow 4b = 7 \Rightarrow b = \frac{7}{4}$ 6. **Final answer:** The solutions are $$b = 0$$ and $$b = \frac{7}{4}$$.