The problem is to solve the equation $\frac{3}{5x+6} = \frac{5}{5x-10}$ for $x$.

1. Problem Description

The problem is to solve the equation $\frac{3}{5x+6} = \frac{5}{5x-10}$ for $x$.

2. Solution Steps

To solve the equation $\frac{3}{5x+6} = \frac{5}{5x-10}$, we can cross-multiply.

$3(5x-10) = 5(5x+6)$

Now, distribute the constants on both sides:

$15x - 30 = 25x + 30$

Next, we want to isolate the $x$ terms on one side and the constant terms on the other side. Subtract $15x$ from both sides:

$-30 = 10x + 30$

Subtract 30 from both sides:

$-60 = 10x$

Finally, divide both sides by 10:

$x = -6$

3. Final Answer

$x = -6$