Minimization of a function with exponential and 2nd degree polynomial

I would like to minimize the following function (from $\mathbb{R}$ to $\mathbb{R}$):$$f(x) = -2a(1+x)\exp(-\Vert xb-c \Vert^2) + (1+x)^2 d$$where $a,d \in \mathbb{R}$ and $b,c \in \mathbb{R}^d$

So first, i tried working with a simplified version of this function :$$g(x) = -(1+x)\exp(-(2x+1)^2) + (1+x)^2 $$

I computed the derivative in order to find the critical points.

$$g'(x)=\exp(-(2x+1)^2) (8x^2+12x+3) + 2(1+x)$$

But i have no idea how to find the critical points g'(x)=0. Since the function is coercive and continuous a global minimum exists here. I'm not even sure there exists a closed form for the minimum (probably not).