Answer
$b=\dfrac{2A-hB}{h}$
Work Step by Step
Using the properties of equality, in terms of $
b
,$ the given equation, $
A=\dfrac{1}{2}h(b+B)
,$ is equivalent to
\begin{array}{l}\require{cancel}
2A=h(b+B)
\\\\
2A=hb+hB
\\\\
2A-hB=hb
\\\\
\dfrac{2A-hB}{h}=\dfrac{hb}{h}
\\\\
\dfrac{2A-hB}{h}=b
\\\\
b=\dfrac{2A-hB}{h}
.\end{array}