Product is 20 the sum is -12

Let one number be x
Let another number be y
ATQ
x + y = -12 => y = -x -12 {mark as the first  equation}
xy = 20 { mark as the second equation} 

Substituting value of y in second equation
x( -x - 12) = 20
-x² - 12x = 20
-x² - 12x - 20 = 0 { middle  term splitting}
-x² -10x - 2x -20 = 0
-x( x + 10 ) -2 ( x +10 ) 
( -x - 2 ) ( x + 10 ) are the factors.
 -x -2 = 0                  x + 10 = 0 
-x = 2                        x = -10
x = -2    
so we get two values of x i.e. -2 and -10
 now substituting value of x in first equation ( x = -2 )
 y = -x - 12                    y = -x - 12
 y = - ( -2 ) - 12             y = -(-10) - 12
 y = 2 - 12                     y = 10 - 12
 y = -10                         y = -2

So we  get to know that if x = -2 then y = -10 And when x = -10 then y = -10.
Hope this help  :)

Chope you get it right gl