If 2 numbers multiply to give you -140 then one of the numbers must be negative. Let's just say x is negative. If that's the case, then -xy = -140. And if those same 2 numbers add to give -31, then -x + y = -31. Solve the second equation for y to get y = x - 31. Sub in that y value into the first equation to get -x(x - 31) = -140. Distributing and then changing all the signs to avoid a negative leading coefficient gives you the quadratic
which factors nicely into x = 4 and x = -35. Our x value has to be the positive one because we determined that x is negative (negative of a negative gives you a positive) so the x value is 4. If you sub that into x in the first equation, you get -4y = -140 and y = 35. So there you go!