The problem asks us to find the solutions to two factored quadratic equations using the Zero Product Property. The given equations are $(v-6)(v-1) = 0$ and $(4x-3)(x+4) = 0$.

1. Problem Description

The problem asks us to find the solutions to two factored quadratic equations using the Zero Product Property. The given equations are $(v-6)(v-1) = 0$ and $(4x-3)(x+4) = 0$.

2. Solution Steps

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

For problem 3, we have $(v-6)(v-1) = 0$.

Applying the Zero Product Property:

$v - 6 = 0$ or $v - 1 = 0$

Solving for $v$ in each case:

$v = 6$ or $v = 1$

Thus, the solutions for problem 3 are $v = 6$ and $v = 1$.

For problem 4, we have $(4x-3)(x+4) = 0$.

Applying the Zero Product Property:

$4x - 3 = 0$ or $x + 4 = 0$

Solving for $x$ in each case:

$4x = 3$ which means $x = \frac{3}{4}$

$x = -4$

Thus, the solutions for problem 4 are $x = \frac{3}{4}$ and $x = -4$.

3. Final Answer

The solutions for the equation $(v-6)(v-1) = 0$ are $v = 6$ and $v = 1$.

The solutions for the equation $(4x-3)(x+4) = 0$ are $x = \frac{3}{4}$ and $x = -4$.