Answer :
We want to simplify
$$
(6x - 5)\left(2x^2 - 3x - 6\right).
$$
**Step 1: Distribute each term from the first polynomial to each term in the second polynomial.**
Multiply the term $6x$ by each term in the second polynomial:
\[
\begin{aligned}
6x \cdot 2x^2 &= 12x^3,\\[1mm]
6x \cdot (-3x) &= -18x^2,\\[1mm]
6x \cdot (-6) &= -36x.
\end{aligned}
\]
Next, multiply the term $-5$ by each term in the second polynomial:
\[
\begin{aligned}
-5 \cdot 2x^2 &= -10x^2,\\[1mm]
-5 \cdot (-3x) &= 15x,\\[1mm]
-5 \cdot (-6) &= 30.
\end{aligned}
\]
**Step 2: Combine like terms.**
Now, add the results from both distributions:
- The $x^3$ term:
$$
12x^3 \quad (\text{only one term}).
$$
- The $x^2$ terms:
$$
-18x^2 + (-10x^2) = -28x^2.
$$
- The $x$ terms:
$$
-36x + 15x = -21x.
$$
- The constant term:
$$
30.
$$
**Step 3: Write the final simplified expression.**
The simplified expression is:
$$
12x^3 - 28x^2 - 21x + 30.
$$
**Conclusion:**
The correct answer is
$$
\boxed{12x^3 - 28x^2 - 21x + 30}.
$$
$$
(6x - 5)\left(2x^2 - 3x - 6\right).
$$
**Step 1: Distribute each term from the first polynomial to each term in the second polynomial.**
Multiply the term $6x$ by each term in the second polynomial:
\[
\begin{aligned}
6x \cdot 2x^2 &= 12x^3,\\[1mm]
6x \cdot (-3x) &= -18x^2,\\[1mm]
6x \cdot (-6) &= -36x.
\end{aligned}
\]
Next, multiply the term $-5$ by each term in the second polynomial:
\[
\begin{aligned}
-5 \cdot 2x^2 &= -10x^2,\\[1mm]
-5 \cdot (-3x) &= 15x,\\[1mm]
-5 \cdot (-6) &= 30.
\end{aligned}
\]
**Step 2: Combine like terms.**
Now, add the results from both distributions:
- The $x^3$ term:
$$
12x^3 \quad (\text{only one term}).
$$
- The $x^2$ terms:
$$
-18x^2 + (-10x^2) = -28x^2.
$$
- The $x$ terms:
$$
-36x + 15x = -21x.
$$
- The constant term:
$$
30.
$$
**Step 3: Write the final simplified expression.**
The simplified expression is:
$$
12x^3 - 28x^2 - 21x + 30.
$$
**Conclusion:**
The correct answer is
$$
\boxed{12x^3 - 28x^2 - 21x + 30}.
$$
