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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