Let's solve the equation step by step:

\[
6 + 12(x + 3) = 7x + 30 + 6x
\]

### Step 1: Expand both sides
Distribute the \( 12 \) on the left-hand side:

\[
6 + 12x + 36 = 7x + 30 + 6x
\]

This simplifies to:

\[
12x + 42 = 7x + 6x + 30
\]

### Step 2: Combine like terms
On the right-hand side, combine \( 7x \) and \( 6x \):

\[
12x + 42 = 13x + 30
\]

### Step 3: Move all terms with \( x \) to one side
Subtract \( 12x \) from both sides:

\[
42 = x + 30
\]

### Step 4: Isolate \( x \)
Subtract 30 from both sides:

\[
x = 12
\]

### Final Answer:
\[
x = 12
\]

Would you like a more detailed explanation of any of the steps?

Here are 5 related questions to further your understanding:
1. How do you solve an equation with variables on both sides?
2. What is the distributive property, and how is it applied in this equation?
3. Can you solve a similar equation where both sides contain parentheses?
4. How do you check if a solution is correct for an equation?
5. What changes in the approach when solving quadratic equations?

**Tip:** Always combine like terms and simplify both sides of an equation before isolating the variable.

Discover how to solve the linear equation 6 + 12(x + 3) = 7x + 30 + 6x with a detailed step-by-step breakdown. This problem focuses on key algebraic concepts such as the distributive property and combining like terms, suitable for students in Grades 8-10.

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