3q^2 -38q-13=0
Factorise the quadratic trinomial.
Find factors of 3 and 13 whose products differ by 38
Note that both 3 and 13 are prime numbers, so there are not many combinations to try.
" "3 and 13
" "darr" "darr
" "1" "13" "rarr 3xx13 = 39
" "3" "1" "rarr 1 xx 3 rarr = ul1
color(white)(xxxxxxxxxxxxxxxxxxx)38larr the difference
These are the correct factors, now put in the signs:
" "3 and 13
" "darr" "darr
" "1" "-13" "rarr 3xx-13 = -39
" "3" "+1" "rarr 1 xx +3 rarr = +ul1
color(white)(xxxxxxxxxxxxxxxxxxxxxx)-38larr the difference
(q-13)(3q+1)=0
Set each factor equal to 0
If q-13=0, rarr q=13
If 3q+1=0, rarr q = -1/3