Let's solve the equation:

\[
3(2n + 5) = 2n - 8
\]

### Step 1: Expand the left side.
Distribute the 3 across the terms inside the parentheses:

\[
3 \times 2n + 3 \times 5 = 6n + 15
\]

Now the equation becomes:

\[
6n + 15 = 2n - 8
\]

### Step 2: Move all terms with \(n\) to one side.
Subtract \(2n\) from both sides to get:

\[
6n - 2n + 15 = -8
\]

Simplifying:

\[
4n + 15 = -8
\]

### Step 3: Move the constant term to the other side.
Subtract 15 from both sides:

\[
4n = -8 - 15
\]

Simplifying:

\[
4n = -23
\]

### Step 4: Solve for \(n\).
Divide both sides by 4:

\[
n = \frac{-23}{4}
\]

Thus, the solution is:

\[
n = -\frac{23}{4}
\]

Would you like any further clarification or details?

### Related Questions:
1. How would the process change if the constants were different?
2. Can you solve a similar equation where fractions are involved?
3. What happens if the variable appears on both sides with different coefficients?
4. How do you check if the solution is correct?
5. What is the impact of negative numbers in equations like this?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure it satisfies both sides.

Learn how to solve the linear equation 3(2n+5) = 2n-8 with a detailed step-by-step guide. This problem covers key algebraic concepts such as the distributive property and solving for variables. Suitable for students in Grades 6-8.

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