How to make a matrix not invertible

A= k+6 5 -3
k+ 4 k+4 1
k+6 5 k-7

for what values of k is the matrix A not invertible?
i know that the det = 0 for it to not be invertible, but can someone show me the math. i have done this problem many times and I still seem to be getting it wrong
can someone show me how to do this?

row3 - row1:
k+6 5 -3
k+ 4 k+4 1
0 0 k-4
(k-4)[(k+6)(k+4) - 5(k+4)] = 0
k = 4
or
k^2 + 5k + 4 = (k+1)(k+4) = 0
k = -1, -4