This is a quadratic equation in the form $ax^2 + bx + c = 0$, where $a=3$, $b=2$, and $c=6$. To simplify or solve this equation, we can use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Step 1: Substitute the values of a, b, and c into the quadratic formula. $$x = \frac{-(2) \pm \sqrt{(2)^2 - 4(3)(6)}}{2(3)}$$ Step 2: Simplify the expression under the square root (the discriminant). $$x = \frac{-2 \pm \sqrt{4 - 72}}{6}$$ $$x = \frac{-2 \pm \sqrt{-68}}{6}$$ Step 3: Simplify the square root of the negative number. We can write $\sqrt{-68}$ as $\sqrt{68}i$, where $i$ is the imaginary unit ($i = \sqrt{-1}$). $$x = \frac{-2 \pm \sqrt{68}i}{6}$$ Step 4: Simplify $\sqrt{68}$. Since $68 = 4 \times 17$, we have $\sqrt{68} = \sqrt{4 \times 17} = 2\sqrt{17}$. $$x = \frac{-2 \pm 2\sqrt{17}i}{6}$$ Step 5: Divide both terms in the numerator by the denominator. $$x = \frac{-2}{6} \pm \frac{2\sqrt{17}i}{6}$$ $$x = -\frac{1}{3} \pm \frac{\sqrt{17}}{3}i$$ The solutions are complex numbers. The simplified form of the equation is: $$x = -\frac{1}{3} \pm \frac{\sqrt{17}}{3}i$$