To solve the equation \((x + \frac{4}{9})(x - \frac{11}{5}) = 0\), we can use the property that if the product of two factors is zero, then at least one of the factors must be zero.

This gives us two separate equations to solve:

1. \(x + \frac{4}{9} = 0\)
2. \(x - \frac{11}{5} = 0\)

**Solving the first equation:**

\[
x + \frac{4}{9} = 0
\]

Subtract \(\frac{4}{9}\) from both sides:

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

**Solving the second equation:**

\[
x - \frac{11}{5} = 0
\]

Add \(\frac{11}{5}\) to both sides:

\[
x = \frac{11}{5}
\]

The solutions to the equation \((x + \frac{4}{9})(x - \frac{11}{5}) = 0\) are:

\[
x = -\frac{4}{9} \quad \text{and} \quad x = \frac{11}{5}
\]