Answer
The solutions are $x=\sqrt{5},$ $x=-\sqrt{5}$ and $x=2$
Work Step by Step
$x^{3}-2x^{2}-5x+10=0$
On the left side of the equation, group the first two and the last two terms together:
$(x^{3}-2x^{2})-(5x-10)=0$
Take out common factor $x^{2}$ from the first parentheses and common factor $5$ from the second one:
$x^{2}(x-2)-5(x-2)=0$
Take out common factor $x-2$
$(x-2)(x^{2}-5)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x-2=0$
$x=2$
$x^{2}-5=0$
$x^{2}=5$
$x=\pm\sqrt{5}$
The solutions are $x=\sqrt{5},$ $x=-\sqrt{5}$ and $x=2$