To solve the inequality 3(5x+1)-5(3x+1) > x, we first simplify the expression:

15x + 3 - 15x - 5 > x
3 > x

So the solution to the inequality is x < 3.

Next, to solve the inequality (x-3)(x+6) < 0, we first find the critical points by setting the expression equal to 0:

(x-3)(x+6) = 0
x = 3 or x = -6

Now we can test each interval on the number line created by the critical points to determine where the expression is less than 0:

For x < -6:
(x-3)(x+6) < 0 is not satisfied.

For -6 < x < 3:
(-6-3)(-6+6) < 0 is not satisfied.

For x > 3:
(3-3)(3+6) < 0 is not satisfied.

Therefore, the solution to the inequality (x-3)(x+6) < 0 is -6 < x < 3.