Let's simplify the given expression step-by-step to find the equivalent expression. The given expression is:
[tex]\[
(3y - 4)(2y + 7) + 11y - 9
\][/tex]
To simplify this, we follow these steps:
1. Distribute the terms within the first part of the expression, [tex]\((3y - 4)(2y + 7)\)[/tex]:
[tex]\[
(3y - 4)(2y + 7) = 3y \cdot 2y + 3y \cdot 7 - 4 \cdot 2y - 4 \cdot 7
\][/tex]
Calculate each term:
[tex]\[
3y \cdot 2y = 6y^2
\][/tex]
[tex]\[
3y \cdot 7 = 21y
\][/tex]
[tex]\[
-4 \cdot 2y = -8y
\][/tex]
[tex]\[
-4 \cdot 7 = -28
\][/tex]
So, the expression [tex]\((3y - 4)(2y + 7)\)[/tex] simplifies to:
[tex]\[
6y^2 + 21y - 8y - 28
\][/tex]
Combine like terms:
[tex]\[
6y^2 + (21y - 8y) - 28 = 6y^2 + 13y - 28
\][/tex]
2. Combine the simplified part with the remaining terms of the original expression, [tex]\((6y^2 + 13y - 28) + 11y - 9\)[/tex]:
First, combine the like terms [tex]\(13y\)[/tex] and [tex]\(11y\)[/tex]:
[tex]\[
6y^2 + 13y + 11y - 28 - 9
\][/tex]
Simplify:
[tex]\[
6y^2 + 24y - 37
\][/tex]
So, the simplified expression is:
[tex]\[
6y^2 + 24y - 37
\][/tex]
Thus, the correct answer is:
C. [tex]\(\boxed{6y^2 + 24y - 37}\)[/tex]
