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To solve this exercise and factorize \( C \), let's begin by substituting \( x = -2 \) into the given expression for \( C \).

The expression for \( C \) is:

\[
C = -3x(4 - 5x) + (4 - 5x)(-3 - 4x)
\]

### Step 1: Substitute \( x = -2 \) into the equation
We substitute \( x = -2 \) into both parts of the expression.

- For \( -3x(4 - 5x) \):

\[
-3(-2)(4 - 5(-2)) = 6(4 + 10) = 6(14) = 84
\]

- For \( (4 - 5x)(-3 - 4x) \):

\[
(4 - 5(-2))(-3 - 4(-2)) = (4 + 10)(-3 + 8) = 14(5) = 70
\]

### Step 2: Add the two results
Now, sum the two parts:

\[
C = 84 + 70 = 154
\]

So, after substituting \( x = -2 \), the value of \( C \) is \( 154 \). 

However, if you need to factorize the original expression for \( C \), let me know, and I can assist you further in that regard.

Do you want more details on this calculation or on the factorization process?

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Here are 5 related questions that build on this:

1. How do you expand expressions like \( (a + b)(c + d) \)?
2. What happens if we substitute a different value for \( x \) in the expression for \( C \)?
3. How can we check the correctness of the factorization of an algebraic expression?
4. Can \( C \) be simplified further for any specific values of \( x \)?
5. What are some common methods for factorizing quadratic expressions?

**Tip:** When simplifying expressions involving variables, always perform operations inside parentheses first before distributing any constants or variables.

Learn how to factorize the algebraic expression C = -3x(4 - 5x) + (4 - 5x)(-3 - 4x) after substituting x = -2. This problem covers key algebraic concepts and uses substitution to find the value of C.

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