Answer
The solutions are $x=2$, $x=2i$ and $x=-2i$
Work Step by Step
$x^{3}-2x^{2}+4x-8=0$
Group the first two terms and the last two terms together:
$(x^{3}-2x^{2})+(4x-8)=0$
Take out common factor $x^{2}$ from the first parentheses and common factor $4$ from the second parentheses:
$x^{2}(x-2)+4(x-2)=0$
Take out common factor $x-2$ from the left side:
$(x-2)(x^{2}+4)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x-2=0$
$x=2$
$x^{2}+4=0$
$x^{2}=-4$
$\sqrt{x^{2}}=\sqrt{-4}$
$x=\pm2i$
The solutions are $x=2$, $x=2i$ and $x=-2i$
