Let us assume the two numbers to be "x" and "y".
Then
xy = 60
x = 60/y
And
x + y = -16
Putting the value of "x" from the first equation in the second equation we get
x + y = - 16
(60/y) + y = - 16
y2 + 60 = - 16y
y^2 + 16y + 60 = 0
y2 + 10y + 6y + 60 = 0
y(y + 10) + 6(y + 10) = 0
(y + 10) ( y + 6) = 0
Then
y + 10 = 0
y = -10
So
x = 60/y
= - (60/10)
= -6
When
y + 6 = 0
y = - 6
Then
x = 60/y
= - (60/6)
= - 10
So the two unknown numbers are - 6 and - 10.