Answer
$x=\frac{1}{2}$
Work Step by Step
Step 1. Rewrite the equation as $2x^3+3x^2+6x-4=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2,\pm4,\pm\frac{1}{2}$
Step 2. Use synthetic division as shown in the figure to find zero(s) $x=\frac{1}{2}$
Step 3. Use the quotient to find other zeros: $2x^2+4x+8=0$, no real solutions.
