We are asked to solve the equation $(6x+7)(x+1) = 0$ for $x$.

1. Problem Description

We are asked to solve the equation $(6x+7)(x+1) = 0$ for $x$.

2. Solution Steps

To solve the equation $(6x+7)(x+1) = 0$, we set each factor equal to zero.

Case 1: $6x+7 = 0$

Subtract 7 from both sides:

$6x = -7$

Divide by 6:

$x = -\frac{7}{6}$

Case 2: $x+1 = 0$

Subtract 1 from both sides:

$x = -1$

Therefore, the solutions are $x = -\frac{7}{6}$ and $x = -1$.

3. Final Answer

$x = -\frac{7}{6}, -1$