Let's solve the expression step by step:

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

### Step 1: Distribute the constants
Distribute the 6 across the terms inside the first parentheses and the 4 across the terms inside the second parentheses:
\[
6 \times 2x + 6 \times 3 + 4 \times x^2 - 4 \times 5x
\]
\[
12x + 18 + 4x^2 - 20x
\]

### Step 2: Combine like terms
Now, combine the like terms:
\[
4x^2 + (12x - 20x) + 18
\]
\[
4x^2 - 8x + 18
\]

### Final Answer:
The simplified expression is:
\[
4x^2 - 8x + 18
\]

Would you like more details or have any questions?

Here are five related questions you might be interested in:
1. How do you factor quadratic expressions like \(4x^2 - 8x + 18\)?
2. What is the difference between expanding and factoring algebraic expressions?
3. How do you solve quadratic equations like \(4x^2 - 8x + 18 = 0\)?
4. What are the properties of polynomials?
5. How do you find the roots of a quadratic equation using the quadratic formula?

**Tip:** Always check if you can simplify an expression further by factoring or by combining like terms.

Learn how to simplify the polynomial expression 6x(2x + 3) + 4(x^2 - 5x) with a detailed step-by-step solution. This problem covers key algebraic concepts, including distribution of constants and combining like terms. Suitable for students in Grades 8-10.

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