j + 3 = 3(y+3)
j + 3 = 3y + 9..................(i)

j - 6 = (y - 6)^2
j - 6 = y^2 -12y + 36 .......(ii)

j - 6 = y^2 -12y + 36
-j - 3 = -3y - 9
_______________________
-9 = y^2 - 15y +27

0= y^2 - 15y + 36
0 = (y-12)(y-3)
y=12 | y=3

So the daughters age is either 12 or 3.

You can plug in to find the correct one. Or you can just realize the daughter cannot be 3 since one of the equations involves "6 years ago."

So plugging 12 in

j + 3 = 3(12) + 9
j = 42

---------------------- Janice . Daughter-----------------
Age of Janice before 6 yrs = J
Age of Daughter before 6 yrs = x

Janice Current age = J+6
Daughter Current age= x+6

Janice after 3 yrs = J+9
Daughtr after 3 yrs= x+9


given J+9 = 3(x+9) ----> 1 and J= x^2 ---->2

x^2-3x-18=0
x= 6 0r -3 (age cannot be -ve) Therefore x= 6

Janice age before 6 yrs = 6^2 = 36
Current age = 36+6= 42

hope this helps.

That was a much easier approach thanks deepamohn