Answer
$\{-1,0\}$
Work Step by Step
$(x-1)^{2}+3(x-1)+2=0$ Equation $(1)$
Let $u= (x-1) $ Equation $(2)$
Substituting $u$ in Equation $(1)$
$u^{2}+3u+2=0$
Splitting the middle term into two numbers whose product is $2$ and whose sum is, $3$. The numbers are $1$ and $2$
$u^{2}+u+2u+2=0$
$u(u+1)+2(u+1)=0$
$(u+1)(u+2)=0$
$u=-1 $ or $u=-2$
Substituting $u$ values in Equation $(2) $ to find $x$
$x-1 = -1$
$x = -1+1$
$x= 0$
$x-1 = -2$
$x = -2+1$
$x= -1$
Solution set is $\{-1,0\}$
