N^2-5n-24
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-3,8

Step-by-step explanation:

1) we can factor this since this quadratic function is in the form of

ax^2+bx+c

where we need to find out what*what=c

and what+what=b

since c is -24 and b is -5 we need to figure out the factors of -24 which equal -5:

-8+3=-5

and

-8*3=-24

hence -8 and 3 is our factors, next we will substitute them in place of "b"

so

n^2-8n+3n-24

split this equation in two groups:

group 1) n^2-8n

group 2) 3n-24

gcf of group 1= n

so

n(n-8)

gcf of group 2: 3

so

3(n-8)

next take numbers outside of parentheses and group them together:

so (n+3) (n-8)=0

since  anything times 0 is equal to 0, either (n+3) is 0 or (n-8) is 0

so

n+3=0

n=-3

n-8=0

n=8

hence n=-3,8

Hope this helps!