complex numbers

$z = a + bi$ where a and b are real numbers and i is one unit in the imaginary plane.

$2(a + bi) + 3(a - bi) = -25 - 2i$

$2a + 2bi + 3a - 3bi = -25 - 2i$

$5a - bi = -25 - 2i$

The real number parts of the equation are equal and the imaginary parts of the equation are equal:

$5a = -25$

$-bi = -2i$

Now, we can obtain that $a = -5$ and $b= 2$.

Thus, $z = -5 + 2i$.