To solve this quadratic equation, we need to use the zero-product property which states that if the product of two numbers is zero, then at least one of the numbers must be zero.

Given equation: ((5x+8)(3-9x) = 0)

Expanding the equation: (15 - 45x + 24x - 72x^2 = 0)

Combine like terms: (-72x^2 - 21x + 15 = 0)

To solve for x, we can either factor or use the quadratic formula. In this case, we can use the quadratic formula to find the roots:

The quadratic formula is given by: [x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}]

For the quadratic equation (ax^2 + bx + c = 0), the coefficients are:
(a = -72), (b = -21), (c = 15).

Plugging these values into the quadratic formula, we get:
[x = \frac{21 \pm \sqrt{(-21)^2 - 4(-72)(15)}}{2(-72)}]
[x = \frac{21 \pm \sqrt{441 + 4320}}{-144}]
[x = \frac{21 \pm \sqrt{3761}}{-144}]

So the solutions for x are:
[x = \frac{21 + \sqrt{3761}}{-144}] and [x = \frac{21 - \sqrt{3761}}{-144}]