Let's solve the equation for \( n \):

Given:
\[
5n = 2(-2n - 20) + n
\]

### Step 1: Distribute the 2 on the right side of the equation.
\[
5n = 2 \times -2n + 2 \times -20 + n
\]
\[
5n = -4n - 40 + n
\]

### Step 2: Combine like terms on the right side.
\[
5n = (-4n + n) - 40
\]
\[
5n = -3n - 40
\]

### Step 3: Add \( 3n \) to both sides to move all \( n \)-terms to one side.
\[
5n + 3n = -40
\]
\[
8n = -40
\]

### Step 4: Divide both sides by 8 to solve for \( n \).
\[
n = \frac{-40}{8}
\]
\[
n = -5
\]

So, the solution is \( n = -5 \).

Would you like more details on any of these steps or have any questions?

Here are 5 related questions to explore further:
1. What is the process for solving equations with variables on both sides?
2. How do you check the solution of an equation?
3. Can you solve an equation with fractions or decimals?
4. What happens when you solve an equation and get a statement like \(0 = 0\) or \(5 = -5\)?
5. How do you solve a system of equations with two variables?

**Tip:** Always combine like terms and simplify each side of the equation as much as possible before trying to isolate the variable.

Learn how to solve the linear equation 5n = 2(-2n - 20) + n using distributive property and combining like terms. This step-by-step guide explains the solution process in detail, making it ideal for students in Grades 6-8.

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