#n^2+color(red)(2)ncolor(orange)(-24)> 0#
We need to factor this quadratic
We need to find two numbers that add to #2# and multiply to #-24#
#+2#
x#24#
..........
#color(black)(1)color(white)(.)color(black)(24)#
#color(black)(2)color(white)(.)color(black)(12)#
#color(black)(3)color(white)(.)color(black)(8)#
#color(green)(4)color(white)(.)color(green)(6)#
#4# and #6# can be combined to form #2#, but we'll need to subtract them.
We are looking for one positive number and one negative number. We can tell because #-24# can only be the product of one positive and negative number.
Now we just need to see if #-4+6# gives us #color(red)(2)# or if it's #-6+4#:
#-4+6=2#
#-6+4=-2#
So, our numbers are #-4# and #6#, which gives us #(n-4)(n+6)> 0#
We just set each factor to zero and solve:
Case 1
#n-4> 0#
#n>4#
Case 2
#n+6> 0#
#n>6#
