To solve this equation, we need to apply the distributive property and simplify both sides of the equation.

Starting with the left side of the equation:
24x - 6x(13x-9)
= 24x - 6x(13x) + 6x(9)
= 24x - 78x^2 + 54x
= 54x - 78x^2

Now, moving on to the right side of the equation:
-13 - 13x(6x-1)
= -13 - 78x^2 + 13x
= 13x - 78x^2 - 13

Now we can set the two sides of the equation equal to each other:
54x - 78x^2 = 13x - 78x^2 - 13

Now, we can simplify the equation further by combining like terms:
54x - 78x^2 = 13x - 78x^2 - 13
54x = 13x - 13

Next, let's isolate the variable x by moving all terms without x to one side:
54x - 13x = -13
41x = -13

Finally, divide both sides by 41 to solve for x:
x = -13/41

Therefore, the solution to the equation is x = -13/41.