\[x^{2} + 6x - 7 =\]
\[= x^{2} + 6x + 9 - 16 =\]
\[= (x + 3)^{2} - 16 =\]
\[= (x + 3 - 4)(x + 3 + 4) =\]
\[= (x - 1)(x + 7).\]