Solve (c^2-d)(c+sqrt{d})=-2

$$( c ^ { 2 } - d ) ( c + \sqrt { d } ) = - 2$$

Solve for c

$$\left\{\begin{matrix}c=\frac{\sqrt{3}i\sqrt[3]{8d^{\frac{3}{2}}+3\sqrt{81-48d^{\frac{3}{2}}}-27}}{6}-\frac{2i\sqrt{3}\left(8d^{\frac{3}{2}}+3\sqrt{81-48d^{\frac{3}{2}}}-27\right)^{-\frac{1}{3}}d}{3}-\frac{\sqrt[3]{8d^{\frac{3}{2}}+3\sqrt{3}\sqrt{27-16d^{\frac{3}{2}}}-27}}{6}-\frac{2\left(8d^{\frac{3}{2}}+3\sqrt{81-48d^{\frac{3}{2}}}-27\right)^{-\frac{1}{3}}d}{3}-\frac{\sqrt{d}}{3}\text{; }c=\frac{4\left(8d^{\frac{3}{2}}+3\sqrt{3}\sqrt{27-16d^{\frac{3}{2}}}-27\right)^{-\frac{1}{3}}d+\sqrt[3]{8d^{\frac{3}{2}}+3\sqrt{3}\sqrt{27-16d^{\frac{3}{2}}}-27}-\sqrt{d}}{3}\text{; }c=\frac{2i\sqrt{3}\left(8d^{\frac{3}{2}}+3\sqrt{81-48d^{\frac{3}{2}}}-27\right)^{-\frac{1}{3}}d}{3}-\frac{\sqrt{3}i\sqrt[3]{8d^{\frac{3}{2}}+3\sqrt{81-48d^{\frac{3}{2}}}-27}}{6}-\frac{\sqrt[3]{8d^{\frac{3}{2}}+3\sqrt{3}\sqrt{27-16d^{\frac{3}{2}}}-27}}{6}-\frac{2\left(8d^{\frac{3}{2}}+3\sqrt{81-48d^{\frac{3}{2}}}-27\right)^{-\frac{1}{3}}d}{3}-\frac{\sqrt{d}}{3}\text{, }&d\neq 0\\c=-\sqrt[3]{2}\approx -1.25992105\text{; }c=\sqrt[3]{-2}\approx 0.629960525+1.091123636i\text{; }c=\sqrt[3]{2}e^{\frac{5\pi i}{3}}\approx 0.629960525-1.091123636i\text{, }&d=0\end{matrix}\right.$$