Question

Hello, is it possible to have some help with this question? I don't quite understand the solution they are looking for.

Answer 1

`\begin{gathered} n=0 \\ n=-(7)/(2) \end{gathered}`

Given:

`7n(2n+7)=0`

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.

`\begin{gathered} a=0 \\ 7n=0 \\ (7n)/(7)=(0)/(7) \\ n=0 \\ --------- \\ b=0 \\ 2n+7=0 \\ 2n=-7 \\ (2n)/(2)=-(7)/(2) \\ n=-(7)/(2) \end{gathered}`

Therefore, the solutions to the equation are:

`\begin{gathered} n=0 \\ n=-(7)/(2) \end{gathered}`