Answer
$x=5$ or $x=1$ or $x=2$
Work Step by Step
$(x-5)(x^{2}-3x+2)=0\qquad$...apply the principle of zero products.
First part:
$x-5=0$
$x=5$
Second part:
$x^{2}-3x+2=0$
... Searching for two factors of $ac=2$ whose sum is $b=-3,$
we find$\qquad-1$ and $-2.$
Rewrite the middle term and factor in pairs:
$x^{2}-x-2x+2=0$
$x(x-1)-2(x-1)=0$
$(x-1)(x-2)=0\qquad$...apply the principle of zero products.
$x-1=0$ or $x-2=0$
$x=1$ or $x=2$
Type the equation into a graphing utility and see
that the graph intercepts the x-axis at $1,2$ and $5$.
