Answer
$c=\dfrac{43}{2}$
Work Step by Step
Using $a(b+c)=ab+ac$ (or the Distributive Property) and combining like terms, the value of the variable that satisfies the given expression, $
2+3(4+c)=1-5(6-c)
,$ is
\begin{array}{l}\require{cancel}
2+12+3c=1-30+5c
\\\\
3c-5c=1-30-2-12
\\\\
-2c=-43
\\\\
c=\dfrac{-43}{-2}
\\\\
c=\dfrac{43}{2}
.\end{array}
