One of the roots of the equation x^{2}+ kx -6 = 0 is 3, and k is constant. Which is greater: k or -1

Now if you plug in 3 for x you get -1 which makes sense, but when I first did the problem I tried to solve it by factoring the equation and I came up with k= -1 or 1 as shown below.

(x + 3)(x - 2) = x^{2}+ x - 6 here k = 1

(x - 3)(x + 2) = x^{2}- x - 6 here k = -1

where am I going wrong? thank you for the help