To solve the equation

\[
\frac{x - \frac{3}{5}}{-\frac{1}{3}} = \frac{2}{5}\left( \frac{x - \frac{3}{5}}{-\frac{1}{3}} \right) = \frac{2}{5}
\]

we'll proceed by simplifying the left side first.

### Step 1: Simplify the Left Side

Starting with:

\[
\frac{x - \frac{3}{5}}{-\frac{1}{3}} = -3\left(x - \frac{3}{5}\right)
\]

This is simply because dividing by \(-\frac{1}{3}\) is equivalent to multiplying by \(-3\).

### Step 2: Set up the Equation

The left side becomes:

\[
-3\left(x - \frac{3}{5}\right) = \frac{2}{5}
\]

### Step 3: Distribute the \(-3\)

Distributing gives us:

\[
-3x + \frac{9}{5} = \frac{2}{5}
\]

### Step 4: Isolate \(x\)

To isolate \(x\), we can move \(\frac{9}{5}\) to the other side:

\[
-3x = \frac{2}{5} - \frac{9}{5}
\]

Now, simplify the right side:

\[
-3x = \frac{2 - 9}{5} = \frac{-7}{5}
\]

### Step 5: Divide by \(-3\)

Next, we divide both sides by \(-3\):

\[
x = \frac{-7}{5} \cdot \frac{-1}{3} = \frac{7}{15}
\]

### Step 6: Solution

Thus, the solution to the equation is:

\[
\boxed{\frac{7}{15}}
\]