Question

how do you solve this problem using the zero product property: (4x +5)(x + 7) = 0

Answer 1

If:
\[(x-a)(x-b)=0; a,b \ge 0 \implies x=a,x=b\]

Answer 2

So:
\[(4x+5)(x+7)=0 \implies 4x=5\implies x=\frac{5}{4}, x=-7\]

Answer 3

Because:
\[(0)(x)=0 \]
For any x so only one of the factors need be zero.