To solve this equation, we can first expand the expression:

(4x-3)(6x-12)(4.8+0.6x) = 0

Expanding, we get:

(24x^2 - 48x - 18x + 36)(4.8+0.6x) = 0
(24x^2 - 66x + 36)(4.8+0.6x) = 0
115.2x^2 - 316.8x + 172.8 = 0

Now we can solve for x by using the quadratic formula:

x = (-(-316.8) ± sqrt((-316.8)^2 - 4(115.2)(172.8))) / 2(115.2)

x = (316.8 ± sqrt(100502.4 - 7971.84)) / 230.4
x = (316.8 ± sqrt(92530.56)) / 230.4
x = (316.8 ± 304.14) / 230.4

Two possible solutions for x:

x = (316.8 + 304.14) / 230.4 ≈ 2.83
x = (316.8 - 304.14) / 230.4 ≈ 0.255

Therefore, the solutions to the equation are x ≈ 2.83 and x ≈ 0.255.