Let's solve the equation \((3x + 6)(x + 3) = 3x^2 - 192\).

### Step 1: Expand the left side
We will expand \((3x + 6)(x + 3)\).

\[
(3x + 6)(x + 3) = 3x(x + 3) + 6(x + 3)
\]
Expanding both terms:

\[
= 3x^2 + 9x + 6x + 18
\]

So, the left side becomes:

\[
3x^2 + 15x + 18
\]

### Step 2: Write the equation
Now we can write the full equation as:

\[
3x^2 + 15x + 18 = 3x^2 - 192
\]

### Step 3: Simplify the equation
Subtract \(3x^2\) from both sides:

\[
15x + 18 = -192
\]

### Step 4: Solve for \(x\)
Subtract 18 from both sides:

\[
15x = -192 - 18
\]

\[
15x = -210
\]

Now, divide by 15:

\[
x = \frac{-210}{15} = -14
\]

### Final answer:
The solution to the equation is \(x = -14\).

Would you like more details on any step? Here are some related questions:

1. How do you check if \(x = -14\) is the correct solution?
2. How do you expand binomials step by step?
3. What is the method to simplify quadratic equations?
4. What are common mistakes to avoid when solving such equations?
5. Can this equation be solved by factoring?

**Tip:** Always verify the solution by substituting it back into the original equation to ensure correctness.

Discover how to solve the equation (3x+6)(x+3) = 3x^2 - 192 using algebraic expansion and simplification techniques. This step-by-step guide covers key algebra concepts, including the distributive property and solving linear equations. Suitable for students in Grades 8-10.

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