We are given the function $f(x) = 6x^3 + px^2 + 2x - 5$, where $p$ is a constant. We also know that $f(-1) = 0$. We need to find the value of $p$.

1. Problem Description

We are given the function $f(x) = 6x^3 + px^2 + 2x - 5$, where $p$ is a constant. We also know that $f(-1) = 0$. We need to find the value of $p$.

2. Solution Steps

Since $f(-1) = 0$, we can substitute $x = -1$ into the function and set it equal to zero.

$f(-1) = 6(-1)^3 + p(-1)^2 + 2(-1) - 5 = 0$

Now, we simplify the expression:

$6(-1) + p(1) - 2 - 5 = 0$

$-6 + p - 2 - 5 = 0$

$p - 13 = 0$

Solving for $p$, we have:

$p = 13$

3. Final Answer

The value of $p$ is 13.