Let's solve the equation step by step:

Given equation:
\[
-15x + 12 + 3 \cdot (2x - 6) = 3x - (21x - 1) + 2
\]

### Step 1: Distribute the multiplication over the terms inside the parentheses.
\[
-15x + 12 + 3 \cdot 2x - 3 \cdot 6 = 3x - 21x + 1 + 2
\]
\[
-15x + 12 + 6x - 18 = 3x - 21x + 1 + 2
\]

### Step 2: Combine like terms on each side of the equation.
On the left side:
\[
-15x + 6x + 12 - 18 = -9x - 6
\]
On the right side:
\[
3x - 21x + 1 + 2 = -18x + 3
\]

So, the equation now is:
\[
-9x - 6 = -18x + 3
\]

### Step 3: Move all the \(x\) terms to one side and the constants to the other side.
\[
-9x + 18x = 3 + 6
\]
\[
9x = 9
\]

### Step 4: Solve for \(x\).
\[
x = \frac{9}{9} = 1
\]

So, the solution is \(x = 1\).

Do you want details or have any questions? Here are five related questions:

1. How would the solution change if the equation had a different constant term?
2. What if there were fractions instead of whole numbers in the equation?
3. How does the equation change if the sign of one of the terms is flipped?
4. Can this method be used for equations with more complex expressions?
5. What are the common mistakes to avoid when solving similar equations?

**Tip:** Always combine like terms before moving them across the equation to simplify the solving process.

Learn how to solve the equation -15x + 12 + 3(2x - 6) = 3x - (21x - 1) + 2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations, distributive property, combining like terms, and solving linear equations. Suitable for students in Grades 7-9.

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