[tex]{ x }^{ 2 }-10x+9[/tex]
First you should ask, which two numbers add up to -10 and multiply to 9.
-9 and -1 add up to -10 and multiply to 9.
[tex](-9)+(-1)=-10[/tex]
[tex](-9)(-1)=9[/tex]
So we can factor and rewrite like this ;
[tex](x-9)\cdot (x-1)[/tex]
Let's equal it to 0 again.
[tex]\\ (x-9)\cdot (x-1)=0[/tex]
The multiplication of (x-9) and (x-1) is equal to 0
So we should equal them to 0 seperately to find the solution set
[tex]x-9=0\\ \\ x=0+9\\ \\ x=9[/tex]
and
[tex]x-1=0\\ \\ x=0+1\\ \\ x=1[/tex]
The solution set,
[tex]{ x }_{ 1,2 }\quad =\quad \left\{ 9,\quad 1 \right\} [/tex]
