To factor the given expression, we can first factor out a common factor of 6x:

6x(4x^3 + x^2 - 2x - 4) = 0

Next, we can factor the quadratic expression in parentheses using grouping:

4x^3 + x^2 - 2x - 4 = (4x^3 + 4x^2) + (x^2 - 4x) = 4x^2(x + 1) - 2x(x + 2) = 2x(2x + 1)(x - 2)

Therefore, the factored form of the given expression is:

6x(2x)(2x + 1)(x - 2) = 12x^2(2x + 1)(x - 2) = 0

So, the solutions are x = 0, x = -1/2, x = 2.