To solve the equation \( 3 \left( \frac{3}{5} - 5x \right) = \frac{4}{5} - 3x \), we can follow these steps:

1. **Distribute the 3 on the left side:**

\[
3 \times \frac{3}{5} - 3 \times 5x = \frac{4}{5} - 3x
\]

This simplifies to:

\[
\frac{9}{5} - 15x = \frac{4}{5} - 3x
\]

2. **Get all \( x \) terms on one side and constant terms on the other side. Add \( 15x \) to both sides:**

\[
\frac{9}{5} = \frac{4}{5} - 3x + 15x
\]

This simplifies to:

\[
\frac{9}{5} = \frac{4}{5} + 12x
\]

3. **Subtract \( \frac{4}{5} \) from both sides:**

\[
\frac{9}{5} - \frac{4}{5} = 12x
\]

This simplifies to:

\[
\frac{5}{5} = 12x
\]

Which reduces to:

\[
1 = 12x
\]

4. **Now, divide both sides by 12:**

\[
x = \frac{1}{12}
\]

Thus, the solution to the equation is:

\[
\boxed{\frac{1}{12}}
\]