Answer
$c=5$
Work Step by Step
$$\begin{align*}
27&=3c-3(6)-(-3)(2c) &\text{Apply the Distributive Property}\\
27&=3c-18+6c &\text{Simplify.}\\
27&=9c-18 &\text{Combine like terms.}\\
27+18&=9c-18+18 &\text{Add 18 to both sides.}\\
45&=9c &\text{Simplify.}\\
\frac{45}{9}&=\frac{9c}{9} &\text{Divide 9to both sides.}\\
5&=c&\text{Simplify.}
\end{align*}$$
Check the answer by substituting $5$ to the variable in the given equation.
$$\begin{align*}
27&=3c-3(6-2c)\\
27&\stackrel{?}{=}3(5)-3(6-2\cdot5)\\
27&\stackrel{?}{=}15+12\\
27&\stackrel{\checkmark}{=}27
\end{align*}$$
Thus, the solution is $c=5$.
