Let's solve the equation step by step:

### Given equation:
\[
5x - 2x = -6(x - 6) + 3(x - 2)
\]

### Step 1: Simplify both sides
On the left-hand side:
\[
5x - 2x = 3x
\]

On the right-hand side:
Distribute the \(-6\) and \(3\) across the terms in the parentheses:
\[
-6(x - 6) = -6x + 36
\]
\[
3(x - 2) = 3x - 6
\]
So, the right-hand side becomes:
\[
-6x + 36 + 3x - 6
\]

### Step 2: Combine like terms
On the right-hand side:
\[
-6x + 3x = -3x
\]
\[
36 - 6 = 30
\]
So, the right-hand side simplifies to:
\[
-3x + 30
\]

### Step 3: Set up the simplified equation
Now we have:
\[
3x = -3x + 30
\]

### Step 4: Move all terms involving \(x\) to one side
Add \(3x\) to both sides:
\[
3x + 3x = 30
\]
\[
6x = 30
\]

### Step 5: Solve for \(x\)
Divide both sides by 6:
\[
x = \frac{30}{6}
\]
\[
x = 5
\]

### Final answer:
\[
x = 5
\]

Do you need more details on any of the steps?

Here are 5 related questions:
1. How do you solve equations with multiple variables?
2. How can you check if a solution to an equation is correct?
3. What are the common properties of linear equations?
4. How does distribution work in algebraic expressions?
5. What happens if an equation has no solution?

**Tip:** When solving equations, always combine like terms and simplify both sides as much as possible before solving for the variable.

Explore the step-by-step solution to solve the linear equation 5x-2x=-6(x-6)+3(x-2). Learn about key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 6-8.

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