To solve this equation, we will need to find a common denominator for the fractions on both sides of the equation.

First, let's multiply both sides by (x+2)(x-3) to eliminate the fractions:

(x+2)(x-3)(5x-2)/(x+2) = (x+2)(x-3)(6x-21)/(x-3)

5x-2 = 6x^2 -15x -12x + 42

Now, we will simplify the equation:

5x-2 = 6x^2 - 27x + 42

Rearranging terms and setting equal to zero:

6x^2 - 32x + 44 = 0

Now, we will solve for x by factoring or using the quadratic formula.