We need to solve the equation $\frac{x+6}{x+4} = \frac{-5}{3x}$ for $x$.

1. Problem Description

We need to solve the equation $\frac{x+6}{x+4} = \frac{-5}{3x}$ for $x$.

2. Solution Steps

First, we cross-multiply to eliminate the fractions:

$3x(x+6) = -5(x+4)$

Expanding both sides:

$3x^2 + 18x = -5x - 20$

Move all terms to one side to form a quadratic equation:

$3x^2 + 18x + 5x + 20 = 0$

$3x^2 + 23x + 20 = 0$

Now, we can factor the quadratic equation:

$(3x + 8)(x + \frac{20}{3})=0$

However, the provided equation is

$(3x+8)(x+2.5)=0$

Or you can factor $3x^2+23x+20 = (3x+8)(x+5)$

$(3x+8)(x+5)=0$

The solutions for x are:

$3x + 8 = 0 => 3x = -8 => x = -\frac{8}{3}$

$x + 5 = 0 => x = -5$

So, the solutions are $x = -\frac{8}{3}$ and $x = -5$.

3. Final Answer

$x = -\frac{8}{3}, -5$