Answer
$x=-1$ or $x=-6$
Work Step by Step
$(x+1)(2x+5)=-1\qquad$...apply the FOIL method.
$ x^{2}+5x+2x+5=-1\qquad$... add $1$ to both sides.
$x^{2}+7x+6=0$
... Searching for two factors of $ac=6$ whose sum is $b=7,$
we find$\qquad 1$ and $6.$
Rewrite the middle term and factor in pairs:
$x^{2}+x+6x+6=0$
$x(x+1)+6(x+1)=0$
$(x+1)(x+6)=0\qquad$...apply the principle of zero products.
$x+1=0$ or $x+6=0$
$x=-1$ or $x=-6$
Type the equation into a graphing utility and see
that the graph intercepts the x-axis at $-1$ and $-6$.
