Two numbers, $$a$$ and $$b$$, are such that the quadratic equation $$a x^2 + 3x + 2b = 0$$ has roots whose sum is $$-6$$ and product is $$-6$$. Determine the value of $$a + b$$.

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The quadratic equation is given as $$a x^2 + 3x + 2b = 0$$. Using the relationships between the coefficients and the roots of a quadratic equation:

- The sum of the roots is given by $$-b/a = -6$$.
- The product of the roots is given by $$c/a = -6$$.

From $$-b/a = -6$$, substituting $$b = 3$$, we find $$a = \frac{1}{2}$$.

Next, using $$c/a = -6$$, substituting $$c = 2b$$, we solve for $$b = -1.5$$.

Finally, adding $$a + b = \frac{1}{2} - 1.5 = -1$$.

Thus, the value of $$a + b$$ is **$$-1$$**.

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