To solve the equation (2x+5)(4x-9) = 0, we can set each factor equal to zero and solve for x.

Setting 2x+5 = 0:
2x = -5
x = -5/2

Setting 4x-9 = 0:
4x = 9
x = 9/4

Therefore, the solutions to the equation are x = -5/2 and x = 9/4.