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Let's solve the equation step-by-step:

### Equation
\[
27 = 3c - 3(6 - 2c)
\]

### Step 1: Distribute the \(-3\) on the right side
\[
27 = 3c - 3 \cdot 6 + 3 \cdot 2c
\]
\[
27 = 3c - 18 + 6c
\]

### Step 2: Combine like terms on the right side
\[
27 = (3c + 6c) - 18
\]
\[
27 = 9c - 18
\]

### Step 3: Add 18 to both sides to isolate terms with \(c\)
\[
27 + 18 = 9c
\]
\[
45 = 9c
\]

### Step 4: Divide both sides by 9 to solve for \(c\)
\[
c = \frac{45}{9}
\]
\[
c = 5
\]

### Solution
The solution is:
\[
c = 5
\]

Would you like more details on any specific step, or have any other questions?

Here are some related questions to explore further:
1. How would the solution change if the equation were \(27 = 3c + 3(6 - 2c)\)?
2. Can we solve for \(c\) in terms of another variable if a term with a different variable were added?
3. What are the steps to solve similar linear equations with parentheses and distribution?
4. How do you solve a linear equation if there are terms on both sides of the equation?
5. How does distribution affect the sign of terms inside parentheses?

**Tip:** Always simplify the equation by performing distribution and combining like terms before isolating the variable.

Learn how to solve the linear equation 27 = 3c - 3(6 - 2c) with a detailed step-by-step solution. This problem involves key algebraic concepts like distribution and combining like terms. Suitable for students in Grades 7-9.

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