Determine the maximum possible value of \[ \frac{\left(x^2+5x+12\right)\left(x^2+5x-12\right)\left(x^2-5x+12\right)\left(-x^2+5x+12\right)}{x^4} \] over all non-zero real numbers $x$.

Let's think step by step and output the final answer within \boxed{}.
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