1. **State the problem:** Solve for $v$ in the equation $$(v^2 - 3v - 4)(4v - 4) = 0.$$\n\n2. **Use the zero product property:** If a product of two factors equals zero, then at least one of the factors must be zero. So, set each factor equal to zero:\n$$v^2 - 3v - 4 = 0$$\nand\n$$4v - 4 = 0.$$\n\n3. **Solve the quadratic equation:** $$v^2 - 3v - 4 = 0.$$\nFactor the quadratic:\n$$v^2 - 3v - 4 = (v - 4)(v + 1) = 0.$$\nSet each factor equal to zero:\n$$v - 4 = 0 \Rightarrow v = 4,$$\n$$v + 1 = 0 \Rightarrow v = -1.$$\n\n4. **Solve the linear equation:** $$4v - 4 = 0.$$\nAdd 4 to both sides:\n$$4v - \cancel{4} + \cancel{4} = 0 + 4,$$\nwhich simplifies to\n$$4v = 4.$$\nDivide both sides by 4:\n$$\frac{4v}{\cancel{4}} = \frac{4}{\cancel{4}} \Rightarrow v = 1.$$\n\n5. **Final answer:** The solutions for $v$ are $$v = 4, v = -1, \text{ and } v = 1.$$