If the absolute maximum value of the function $f\left(x\right)=(x^2-2x+7)e^{(4x^3-12x^2-180x+31)}$ in the interval $[-3,0]isf\left(\alpha \right),$ then

$f\text{'}\left(x\right)=e^{(4x^3-12x^2-180x+31)}\left((x^2-2x+7)\right)$

$((12x^2-24x-180)+2(x-1))$

$f\text{'}\left(x\right)=e^{(4x^3-12x^2-180+31)}12\left({(x-1)}^2+6)\right)$

$(x-5)(x+3)+2(x-1))$

Clearly, for $x\in [-3,0],f\left(x\right)<0.$

So, $f\left(x\right)$ is decreasing function on [-3, 0].

Therefore, the absolute maximum value of the function $f\left(x\right)$ is at $x=-3.$

$\Rightarrow \alpha =-3$