Solve (x+1)(x-3)(x+7)(-7)=0: Finding All Solutions Using Zero Product Property

Let's solve the following equation:

$-7(x+1)(x-3)(x+7)=0$

First, let's divide both sides of the equation by the number outside of the parentheses:

$-7(x+1)(x-3)(x+7)=0 \hspace{6pt}\text{/}:(-7)\\ (x+1)(x-3)(x+7)=0$

Remember that the product of an expression equals 0 only if at least one of the multiplying expressions equals zero,

Therefore we should obtain three simple equations and solve them by isolating the variable in each one:

$x+1=0\\ \boxed{x=-1}$or:

$x-3=0\\ \boxed{x=3}$or:

$x+7=0\\ \boxed{x=-7}$ Hence the solution to the equation is:

$\boxed{x=-1,3-7}$The correct answer is answer D.