Let's begin by listing out the information given to us:
[tex]\begin{gathered} -3w+27=6 \\ \text{Put like terms together, we have:} \\ \text{Add 3w to both sides, we have:} \\ -3w+3w+27=6+3w \\ 27=6+3w \\ \text{Subtract 6 from both sides, we have:} \\ 27-6=6-6+3w \\ 21=3w\Rightarrow3w=21 \\ \frac{3w}{3}=\frac{21}{3}\Rightarrow w=7 \\ w=7 \end{gathered}[/tex]
