Solve z^3+(3-2i)z^2+(1-4i)z-1-2i=0

$$z ^ { 3 } + ( 3 - 2 i ) z ^ { 2 } + ( 1 - 4 i ) z - 1 - 2 i = 0$$

Solve for z

$$z=-\frac{\sqrt[3]{2}\left(1+\sqrt{3}i\right)\left(3\sqrt{3}i+5i\right)^{-\frac{1}{3}}\left(2^{\frac{2}{3}}\left(-2-3i\right)\sqrt[3]{3\left(5\sqrt{3}i+9i\right)}+2^{\frac{2}{3}}\left(3-2i\right)\sqrt[3]{3\sqrt{3}i+5i}-2\sqrt{3}i\left(3\sqrt{3}i+5i\right)^{\frac{2}{3}}-2\left(3\sqrt{3}i+5i\right)^{\frac{2}{3}}+4\sqrt[3]{2}\right)}{24}\approx -2+i$$

$$z=\frac{\left(3\sqrt{3}i+5i\right)^{-\frac{1}{3}}\left(\sqrt[3]{2}\left(\left(3\sqrt{3}i+5i\right)^{\frac{2}{3}}+\sqrt[3]{2}\right)+\left(-3+2i\right)\sqrt[3]{3\sqrt{3}i+5i}\right)}{3}\approx i$$

$$z=-\frac{\sqrt[3]{2}\left(-\sqrt{3}i+1\right)\left(3\sqrt{3}i+5i\right)^{-\frac{1}{3}}\left(2^{\frac{2}{3}}\left(2+3i\right)\sqrt[3]{3\left(5\sqrt{3}i+9i\right)}+2^{\frac{2}{3}}\left(3-2i\right)\sqrt[3]{3\sqrt{3}i+5i}+2\sqrt{3}i\left(3\sqrt{3}i+5i\right)^{\frac{2}{3}}-2\left(3\sqrt{3}i+5i\right)^{\frac{2}{3}}+4\sqrt[3]{2}\right)}{24}\approx -1+6.695003253 \cdot 10^{-17}i$$