To solve this equation, we need to expand the left side of the equation and then set it equal to the right side of the equation.

First, let's expand the left side of the equation using the distributive property:

(5x - 2)(x + 3) = 5x^2 + 15x - 2x - 6 = 5x^2 + 13x - 6

Now, we set this expression equal to 13(x-2) and solve for x:

5x^2 + 13x - 6 = 13x - 26
5x^2 + 13x - 6 - 13x + 26 = 0
5x^2 + 20 = 0

Now, we have a quadratic equation. Let's set it equal to zero and solve for x:

5x^2 + 20 = 0
5x^2 = -20
x^2 = -4

Taking the square root of both sides, we get:

x = ±2i

Therefore, the solutions to the equation (5x-2)(x+3) = 13(x-2) are x = 2i and x = -2i.