Find all real numbers a such that equation 3^(x2+2ax+4a−3)−2=|(a−2)/(x+2)| Has exactly two different roots x1,x2 those belong to [−4;0]

Question

Find all real numbers $a$ such that equation $${3^{(x^2+2ax+4a-3)}}-2=|{a-2 \over x+2}|$$ Has exactly two different roots $x_1,x_2 $ those belong to $[-4;0]$
Tried plenty different things to solve:
Analyzing the quadratic equation discriminant wasn't useful. I think that we should consider different cases to open up the modulus, but parameter makes it difficult.
I come to conclusion that my knowledge is not enough to answer that question.
Thank for your help!