Maximizing a function involving a linear combination of the positive and negative part

Question

Let $u:\mathbb{R}_+ \rightarrow \mathbb{R}$ be a differentiable and strictly concave function satisfying $\lim_{x \to 0^+} u(x)=\infty$ and $\lim_{x \to \infty} u(x)=0$, and let $a,b,c \in \mathbb{R}$ with $a$ and $b<0$. I want to know if is possible to find a explicit formula for the $x\geq 0$ which maximize the function $u(x)+(c-x)_+a+(c-x)_-b$, where $(c-x)_+$ and $(c-x)_-$ are the positive and negative parts of $c-x$ respectively.