Expanding the left side of the equation:

(2x-1)(15+9x) - 6x(3x-5)
= 2x(15) + 2x(9x) - 15 - 9x - 6x(3x) + 6x(5)
= 30x + 18x^2 - 15 - 9x - 18x^2 + 30x
= 48x - 15

Setting the expanded expression equal to 87:

48x - 15 = 87

Adding 15 to both sides:

48x = 102

Dividing by 48:

x = 102/48
x = 2.125

Therefore, the solution to the equation is x = 2.125.