Answer
$$d=\frac{2A-2ab}{a+c} .$$
Work Step by Step
To solve the given equation for $d$, we multiply both sides by 2 and then we follow the following steps:
$$ A=ab+\frac{d}{2}(a+c) \Longrightarrow 2A=2ab+d(a+c)\\
\Longrightarrow d(a+c)=2A-2ab\\ \Longrightarrow \frac{d(a+c)}{a+c}=\frac{2A-2ab}{a+c}\\ \Longrightarrow d=\frac{2A-2ab}{a+c} .$$
