Answer
$x=-6,2$
Work Step by Step
Re-write the given equation as: $(e)^{4x} \cdot (e)^{x^2}=e^{12} ...(1)$
We know that $a^{m} \cdot a^n =a^{m+n}$
So, we can write equation (1) as: $e^{4x+x^2}=e^{12}$
Use the power rule: $a^p=a^q$.
We can see that the base $a=e$ is the same on both sides of the equation.
So, the exponents will also be equal.
This implies that $p=q$
Therefore, $4x+x^2=12 \\ x^2+4x-12=0 \\ (x +6)(x-2)=0 $
By the zero-product property, we have: $x=-6,2$
