To solve the complex number equation z^4 + 2z^3 + (2+i)z^2 + (1+3i)z - (3+2i) = 0, we can follow these steps:

Step 1: Rearrange the equation to set it equal to zero: z^4 + 2z^3 + (2+i)z^2 + (1+3i)z - (3+2i) = 0

Step 2: Factor the equation to find possible roots. Unfortunately, there is no simple general method to factor a quartic (degree 4) equation. However, we can use numerical methods or software to find approximate solutions.

Step 3: Use numerical methods or software to solve for the roots of the equation. Solving this quartic equation requires more complex numerical techniques like Newton-Raphson method or polynomial root-finding algorithms.