Let's simplify the expression step by step:

Given:
\[
4(6d + 9) - 5(2d - 10)
\]

1. Distribute the 4 and -5 across the terms inside the parentheses:
\[
4 \times 6d + 4 \times 9 - 5 \times 2d + 5 \times 10
\]
\[
24d + 36 - 10d + 50
\]

2. Combine like terms:
\[
(24d - 10d) + (36 + 50)
\]
\[
14d + 86
\]

So, the simplified expression is:
\[
\boxed{14d + 86}
\]

Would you like more details or have any questions? 

Here are five related questions you might find useful:

1. How would you simplify \(3(2x + 5) - 2(4x - 3)\)?
2. What is the result of distributing in the expression \(7(2a + 4) - 3(5a - 2)\)?
3. How do you solve the equation \(6(3y + 2) = 4(5y - 3)\)?
4. What are the steps to combine like terms in the expression \(8m - 3 + 5m + 7\)?
5. How would you factor the expression \(14d + 86\) back to its original form?

**Tip:** Always distribute the coefficients to all terms within the parentheses before combining like terms to simplify expressions.

Learn how to simplify the algebraic expression 4 times the quantity 6d plus 9, minus 5 times the quantity 2d minus 10, with detailed step-by-step solution. This problem covers key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 7-9.

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