Let's expand both sides of the equation:

Left side:
(x - 2)(x + 2)
= x(x) + x(2) - 2(x) - 2(2)
= x^2 + 2x - 2x - 4
= x^2 - 4

Right side:
3(x + 4)^2 - 2x(x + 5)
= 3(x^2 + 8x + 16) - 2x^2 - 10x
= 3x^2 + 24x + 48 - 2x^2 - 10x
= x^2 + 14x + 48

Now we can set the left and right side equal to each other:
x^2 - 4 = x^2 + 14x + 48

Now we can solve for x:
Subtract x^2 from both sides:
-4 = 14x + 48

Subtract 48 from both sides:
-52 = 14x

Divide by 14:
x = -52/14
x = -26/7

Therefore, the solution to the equation is x = -26/7.