What two numbers multiply to get neg 240 and what two same numbers add to get neg 8

Make the number x & y

x*y=-240240

x+y=-8 < you can rearrange this as x=-8-y

Now substitute in this rearrangement

(-8-y) * y=-240

-8y-y² = - 240 (add y² and 8y)

0=y²+8y-240 (now factorise the equation)

0 = (y+20) (y-12) (for 2 things to multiply and equal zero one or both has to equal zero)

so y+20=0 and/or y-12=0

so y=-20 or y=12

Now substitute these into x+y=-8 to get x

y=-20 then x=12

y=12 then x=-20