Solving a cubic

Algebra Level pending

The two irrational solutions to the equation \(3ix(4-3x^2-2ix)=8\) can be represented as \(\pm \frac{a\sqrt{b}}{c}\), where \(a,b,c\) are positive integers, \(a,c\) are relatively prime, and \(b\) is not divisible by the square of any integer greater than \(1\). Find the product \(abc\).

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