Problem Description:
Given the coordinates of points A(2, -1) and B(-3, -2) in a triangle ABC, and the equation of the angle bisector of angle B, we need to find the equation of line BC.

Approach:
To find the equation of line BC, we will follow the following steps:
1. Find the equation of line AB using the coordinates of points A and B.
2. Find the slope of line AB.
3. Find the slope of the angle bisector of angle B using the given equation.
4. Use the midpoint formula to find the coordinates of point C.
5. Use the coordinates of points B and C to find the equation of line BC.

Solution:
Step 1: Find the equation of line AB
The equation of a line passing through points (x1, y1) and (x2, y2) is given by:
(y - y1) = m(x - x1), where m is the slope of the line.
Using the coordinates of points A(2, -1) and B(-3, -2), we can find the equation of line AB as:
(y - (-1)) = [(y2 - y1)/(x2 - x1)](x - 2)
Simplifying the equation, we get:
y + 1 = [-1/5](x - 2)
5y + 5 = -x + 2
x + 5y - 3 = 0

Step 2: Find the slope of line AB
The equation of a line in the form Ax + By + C = 0 can be rewritten as y = (-A/B)x - (C/B).
Comparing the equation of line AB (x + 5y - 3 = 0) with the standard form, we can find the slope of line AB as -A/B = -1/5.

Step 3: Find the slope of the angle bisector of angle B
The given equation of the angle bisector is 3x - 2y + 5 = 0.
Comparing this equation with the standard form, we can find the slope of the angle bisector as -A/B = -3/-2 = 3/2.

Step 4: Use the midpoint formula to find the coordinates of point C
Let the coordinates of point C be (x, y).
The midpoint of line AB is the intersection point of line AB and the angle bisector of angle B.
Using the slope-intercept form of line AB (y = (-1/5)x + 3/5) and the equation of the angle bisector (3x - 2y + 5 = 0), we can solve these equations simultaneously to find the coordinates of point C.

Step 5: Use the coordinates of points B and C to find the equation of line BC
Using the coordinates of points B(-3, -2) and C, we can find the equation of line BC using the point-slope form:
(y - y1) = m(x - x1), where m is the slope of the line.
Substituting the coordinates of point B and the slope of line BC, we get:
(y - (-2))