Answer
$$
e^{x^{2}+5 x+6} =1
$$
The solution of the given equation is
$$
x =-3 \quad \text { or } \quad x=-2.
$$
Work Step by Step
$$
e^{x^{2}+5 x+6} =1
$$
Since the bases must be the same, write 1 as $e^{0}$ giving
$$
\begin{aligned} e^{x^{2}+5 x+6} &=1 \\ e^{x^{2}+5 x+6} &=e^{0} \\ x 2+5 x+6 &=0 \\(x+3)(x+2) &=0 \\ x+3 &=0 \quad \text { or } \quad x+2=0 \\ x &=-3 \quad \text { or } \quad x=-2 \end{aligned}
$$
So, the solution of the given equation is
$$
x =-3 \quad \text { or } \quad x=-2.
$$
