Let's simplify the expression step by step.

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

### Step 1: Distribute \( 3x \) and \( 6x \) across the parentheses.

For the first term \( 3x(5 - 2x) \):
\[
3x(5) = 15x
\]
\[
3x(-2x) = -6x^2
\]
So, \( 3x(5 - 2x) = 15x - 6x^2 \).

For the second term \( 6x(x - 2) \):
\[
6x(x) = 6x^2
\]
\[
6x(-2) = -12x
\]
So, \( 6x(x - 2) = 6x^2 - 12x \).

### Step 2: Combine like terms.
Now we combine all the terms:
\[
15x - 6x^2 + 6x^2 - 12x
\]

Simplify the expression by combining \( -6x^2 \) and \( 6x^2 \), as well as \( 15x \) and \( -12x \):
\[
0x^2 + (15x - 12x) = 3x
\]

### Final simplified expression:
\[
3x
\]

Would you like more details, or do you have any questions?

Here are some related problems:
1. Simplify \( 4x(3 - x) + 5x(x + 1) \).
2. Factor \( 2x^2 + 5x - 3 \).
3. Expand \( (x - 2)(x + 4) \).
4. Solve \( 2x(3x - 4) = 0 \).
5. Find the derivative of \( 3x^2 - 2x + 1 \).

**Tip:** When simplifying expressions, always look for like terms that can be combined to reduce the expression further.

Learn how to simplify the polynomial expression 3x(5 - 2x) + 6x(x - 2) through step-by-step application of the distributive property and combining like terms. This example is perfect for students studying algebra in Grades 8-10.

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