Expanding the expression:
(6x+5)^2 = (6x+5)(6x+5) = 36x^2 + 30x + 30x + 25 = 36x^2 + 60x + 25
-4x(3+9x) = -12x - 36x^2

Now the given expression becomes:
(36x^2 + 60x + 25) - (12x + 36x^2) = 49
36x^2 + 60x + 25 - 12x - 36x^2 = 49
60x + 25 - 12x = 49
48x + 25 = 49
48x = 24
x = 24/48
x = 1/2

Therefore, the solution to the equation is x = 1/2.