Let's simplify the expression step by step:

Given:
\[
3x(x-6) - 5x(2x-4)
\]

### Step 1: Expand the terms
1. Expand \( 3x(x-6) \):
\[
3x \times x = 3x^2
\]
\[
3x \times (-6) = -18x
\]
So, \( 3x(x-6) = 3x^2 - 18x \).

2. Expand \( -5x(2x-4) \):
\[
-5x \times 2x = -10x^2
\]
\[
-5x \times (-4) = 20x
\]
So, \( -5x(2x-4) = -10x^2 + 20x \).

### Step 2: Combine the expanded terms
Now combine the terms from both parts:
\[
(3x^2 - 18x) + (-10x^2 + 20x)
\]

### Step 3: Combine like terms
Combine the \( x^2 \) terms:
\[
3x^2 - 10x^2 = -7x^2
\]

Combine the \( x \) terms:
\[
-18x + 20x = 2x
\]

### Final Simplified Expression:
\[
-7x^2 + 2x
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you factor a quadratic expression like this?
2. What happens if you set \( -7x^2 + 2x = 0 \)?
3. How do you graph the expression \( -7x^2 + 2x \)?
4. What are the solutions to \( -7x^2 + 2x = 0 \)?
5. How does the distributive property work in simplifying algebraic expressions?

**Tip**: Always expand terms carefully and group like terms when simplifying expressions!

Step-by-step solution to simplify the algebraic expression 3x(x-6) - 5x(2x-4). Learn how to expand terms, apply the distributive property, and combine like terms. This problem is ideal for students in Grades 8-10 studying polynomial simplification.

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