Let's solve the equation step by step:

\[
9x - 5(-8x + 3) - 6 = -21
\]

### Step 1: Distribute the \(-5\) across the parentheses:

\[
9x + 40x - 15 - 6 = -21
\]

### Step 2: Combine like terms on the left-hand side:

\[
(9x + 40x) - (15 + 6) = -21
\]
\[
49x - 21 = -21
\]

### Step 3: Add 21 to both sides to isolate the term with \(x\):

\[
49x = 0
\]

### Step 4: Solve for \(x\) by dividing both sides by 49:

\[
x = \frac{0}{49} = 0
\]

### Final Solution: 
\[
x = 0
\]

Would you like a detailed breakdown or further explanation?

Here are some related questions:
1. How do you solve equations with distribution?
2. What is the importance of isolating variables in equations?
3. How do you check if your solution to an equation is correct?
4. What are the steps to solving equations with multiple variables?
5. How does factoring work in algebraic equations?

**Tip:** Always combine like terms early to simplify the equation and reduce the number of steps!

Discover how to solve the linear equation 9x - 5(-8x + 3) - 6 = -21 with step-by-step guidance. This problem focuses on the distributive property, combining like terms, and isolating variables. Suitable for students in Grades 8-10.

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