Let's solve the equation step by step.

The equation is:

\[
6(3a + 1) - 30 = 3(2a - 4)
\]

### Step 1: Distribute the numbers
Distribute 6 on the left-hand side and 3 on the right-hand side:

\[
6 \times 3a + 6 \times 1 - 30 = 3 \times 2a - 3 \times 4
\]

This simplifies to:

\[
18a + 6 - 30 = 6a - 12
\]

### Step 2: Simplify both sides
Now, simplify the constants:

\[
18a - 24 = 6a - 12
\]

### Step 3: Move variable terms to one side
Subtract \(6a\) from both sides:

\[
18a - 6a - 24 = -12
\]

Simplifies to:

\[
12a - 24 = -12
\]

### Step 4: Move constant terms to the other side
Add 24 to both sides:

\[
12a = 12
\]

### Step 5: Solve for \(a\)
Divide both sides by 12:

\[
a = 1
\]

### Final Answer:
\[
a = 1
\]

Would you like further clarification or additional details?

Here are some related questions to expand your understanding:

1. How can you check if the solution to an equation is correct?
2. What is the distributive property, and why is it important in solving equations?
3. How do you solve equations with variables on both sides?
4. What is the difference between solving linear and quadratic equations?
5. Can there be more than one solution to a linear equation?

**Tip:** Always simplify the equation step-by-step and keep the variable terms on one side for clarity!

Learn how to solve the linear equation 6(3a+1)-30=3(2a-4) using the distributive property and algebraic simplification techniques. This step-by-step guide walks through balancing equations and isolating variables. Suitable for students in Grades 6-8.

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