To solve the equation \( k(3x - 2) = 4 - 6x \), let's follow these steps:

1. **Distribute** \( k \) on the left-hand side:
   \[
   k(3x - 2) = k \cdot 3x - k \cdot 2 = 3kx - 2k
   \]
   The equation now becomes:
   \[
   3kx - 2k = 4 - 6x
   \]

2. **Rearrange the equation** to group all terms involving \( x \) on one side and constant terms on the other side:
   \[
   3kx + 6x = 4 + 2k
   \]

3. **Factor out** \( x \) from the terms on the left:
   \[
   x(3k + 6) = 4 + 2k
   \]

4. **Solve for \( x \)**:
   \[
   x = \frac{4 + 2k}{3k + 6}
   \]

Thus, the solution is:
\[
x = \frac{4 + 2k}{3k + 6}
\]

Let me know if you need further details!

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**Related questions:**
1. How do you solve linear equations involving distributive property?
2. What happens if \( k = -2 \)? How does it affect the solution?
3. What would happen if the right-hand side had a quadratic term instead?
4. Can you explain factoring in more detail with other examples?
5. What are the cases when an equation has no solution?

**Tip**: Always check for special values of \( k \) that might simplify or invalidate the solution (like when denominators are zero).

Learn how to solve the linear equation k(3x - 2) = 4 - 6x using the distributive property and factoring. This problem demonstrates key algebraic concepts, perfect for students in Grades 8-10, with a detailed step-by-step solution.

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