Answer
[tex]\begin{gathered} n=0 \\ n=-\frac{7}{2} \end{gathered}[/tex]
Given:
[tex]7n(2n+7)=0[/tex]
The Zero-Product Property states that ab = 0. Either a or b or both must be zero. In the given equation, we can set a and b as:
a = 7n
b = 2n + 7
We will then equate a = 0 and b = 0 to solve the equation.
[tex]\begin{gathered} a=0 \\ 7n=0 \\ \frac{7n}{7}=\frac{0}{7} \\ n=0 \\ --------- \\ b=0 \\ 2n+7=0 \\ 2n=-7 \\ \frac{2n}{2}=-\frac{7}{2} \\ n=-\frac{7}{2} \end{gathered}[/tex]
Therefore, the solutions to the equation are:
[tex]\begin{gathered} n=0 \\ n=-\frac{7}{2} \end{gathered}[/tex]
