X^2 - 19x + 90 = 0 factor and solve

Find what 2 numbers multiply to get 90 and add to get -19

they must be both be negative so
factor 90
90
1,90
2,45
3,30
5,18
9,10

add

1+90=91
2+45=47
3+30=33
5+18=23
9+10=19 correct

numbers are -9 and -10 since negative times negative=positive

so
it factored out to
(x-9)(x-10)=0
set each to zero

x-9=0
add 9
x=9

x-10=0
add 10
x=10

x=9 or 10