Answer
The solutions are -7 and -1.
Work Step by Step
$x^{2}$+8x+7=0
$x^{2}$+x +7x+7=0
x(x+1)+7(x+1)=0
(x+7)(x+1)=0
x+7=0 and x+1=0
x+7-7=0 -7 and x+1-1=0-1
x=-7 and x=-1
Check
Let x=-7
$x^{2}$+8x+7=0
$(-7)^{2}$+8(-7)+7=0
49-56+7=0
0=0
Let x=-1
$x^{2}$+8x+7=0
$(-1)^{2}$+8(-1)+7=0
1-8+7=0
0=0
