Let's expand the left side of the equation first:

4x(x+3) + (2x-3)(2x-5)
= 4x^2 + 12x + 2x(2x) - 3(2x) - 3(2x) + 35
= 4x^2 + 12x + 4x^2 - 6x - 6x + 15
= 8x^2 + 12x - 6x + 15
= 8x^2 + 6x + 15

Now, the right side of the equation is -1 + 8x^2.

Equating the left and right sides:

8x^2 + 6x + 15 = -1 + 8x^2

Rearranging terms:

6x + 15 = -1

Subtracting 15 from both sides:

6x = -16

Dividing by 6:

x = -16/6
x = -8/3

Therefore, the solution to the equation is x = -8/3.