Let's solve the equation:

\[
(2u + 6) + 6u = -(-5u - 3)
\]

### Step 1: Simplify both sides
On the left-hand side, combine like terms:
\[
2u + 6u + 6 = 8u + 6
\]

On the right-hand side, distribute the negative sign:
\[
-(-5u - 3) = 5u + 3
\]

Now, the equation is:
\[
8u + 6 = 5u + 3
\]

### Step 2: Move the variable terms to one side
Subtract \(5u\) from both sides:
\[
8u - 5u + 6 = 5u - 5u + 3
\]
\[
3u + 6 = 3
\]

### Step 3: Move the constant term to the other side
Subtract 6 from both sides:
\[
3u + 6 - 6 = 3 - 6
\]
\[
3u = -3
\]

### Step 4: Solve for \(u\)
Divide both sides by 3:
\[
u = \frac{-3}{3} = -1
\]

### Final Solution:
\[
u = -1
\]

Would you like more details on any step?

Here are 5 questions to further explore the topic:
1. What happens when variables appear on both sides of the equation?
2. How do you handle negative signs during distribution?
3. Can you explain why it's important to isolate the variable?
4. What is the difference between linear and non-linear equations?
5. How can you check if the solution to an equation is correct?

**Tip:** Always double-check your final answer by plugging it back into the original equation to ensure both sides are equal.

Learn how to solve the linear equation (2u + 6) + 6u = -(-5u - 3) using algebraic techniques like combining like terms and distribution. This step-by-step solution is ideal for students in Grades 7-9, covering key concepts of linear equations.

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