Consider the quadratic function defined by the equation:

$$f(x) = ax^2 + bx + c$$

where $a$, $b$, and $c$ are real numbers. If the function has zeros at $x = 2$ and $x = -3$, and if the sum of the coefficients $a$, $b$, and $c$ equals $0$, find the value of $a$. Express your answer as both a decimal and a fraction.