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**Hint:**For answering this question we are asked to solve the given equation $-5n-8\left( 1+7n \right)=-8$ and find the value of the variable $n$. For solving that we will make some transformations and basic arithmetic simplifications and conclude the value of the unknown variable $n$ and this is what we have been asked to do in the question. Firstly we should observe the given equation and bring all the terms containing the unknown variable $n$ one side and the other terms on the other side of the equation and then solve them.

**Complete answer:**

Now considering from the question we have been asked to solve the given equation $-5n-8\left( 1+7n \right)=-8$ and derive the value of an unknown variable $n$ .

After simplifying the given equation by performing basic multiplication arithmetic operation we will have $-5n-8-56n=-8$ .

Firstly we will observe the given equation and bring all the terms containing the unknown variable $n$ one side and the other terms on the other side of the equation.

If we observe the given equation carefully it is already arranged similarly but there is one term more in the left hand side we need to bring it to the right hand side.

After transforming the term $-8$ to right hand from left hand we will have $\Rightarrow -5n-56n=-8+8$

Now by performing basic arithmetic simplifications that are addition for the left hand side terms in this case we will get the equation reduced to $\Rightarrow -61n=-8+8$ .

For further simplification we will perform the basic arithmetic addition for the terms in the right hand side and after that we will have $\Rightarrow -61n=0$ .

Now we will transform the $-61$ from the left hand side to right hand side after this transformation we will have $\Rightarrow n=\dfrac{0}{-61}$ .

Now we will perform the basic arithmetic division operation involved in the right hand side of the equation after that we will have $\Rightarrow n=0$ .

Therefore we can conclude that the value of $n$ in $-5n-8\left( 1+7n \right)=-8$ is $0$ .

**Note:**

This type questions are very simple to answer and less mistakes are probably. We should be sure with our calculations while solving this question and the transformations and basic arithmetic simplifications we make. Similarly we can solve same type of equations for example $\begin{align}

& -2x-6\left( 2+5x \right)=-4\Rightarrow -2x-12-30x=-4\Rightarrow -32x-12=-4\Rightarrow -32x=-4+12\Rightarrow -32x=8 \\

& \Rightarrow x=\dfrac{8}{-32}\Rightarrow x=-\dfrac{1}{4} \\

\end{align}$

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