[tex]-4x^3= 32\\\\\implies x^3 = -\dfrac{32}4\\\\\implies x^3 = -8\\\\\implies x^3 +8 = 0\\\\\implies x^3 +2^3 =0\\\\\implies (x+2)(x^2 -2x +2^2)=0\\\\\implies (x+2)(x^2 -2x +4) = 0\\\\\implies x +2 =0~~~\text{or} ~~~~x^2 -2x +4 = 0\\ \\\implies x = -2 ~~~~~~\text{or} ~~~~ x= \dfrac{2 \pm\sqrt{-12}}{2}=\dfrac{2 \pm i\sqrt{12}}2}=\dfrac{2\pm2i\sqrt3}{2}=1\pm i\sqrt 3\\\\\text{Hence,}~ x = -2,~~ x = 1+i\sqrt 3,~~~ x= 1-i\sqrt3[/tex]
