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!