Answer
$\{-\frac{1}{4}, 6 \}$
Work Step by Step
Step 1. Given $|4x^2-23x-6|=0$, remove the absolute sign to get $4x^2-23x-6=0$
Step 2. Factor and solve: $(x-6)(4x+1)=0$ which gives $x=-\frac{1}{4}, 6$ or $\{-\frac{1}{4}, 6 \}$
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