Answer
$x=\frac{5}{2}$.
Work Step by Step
Step 1. For $2x^3-3x^2-3x-5=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm5,\pm\frac{1}{2},\pm\frac{5}{2}$
Step 2. Use synthetic division as shown in the figure to find zero(s) $x=\frac{5}{2}$.
Step 3. Use the quotient to find other zeros: $2x^2+2x+2=0$ no real solutions.
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