To solve for C let us do these steps
1. Put the term of C on one side and the other terms on the other side
Subtract 32 from both sides to move the term 32 to the other side
[tex]\begin{gathered} F-32=\frac{9}{5}C+32-32 \\ F-32=\frac{9}{5}C \end{gathered}[/tex]2. Make the coefficient of C = 1
Divide both sides by 9/5
[tex]\begin{gathered} \frac{F-32}{\frac{9}{5}}=\frac{\frac{9}{5}C}{\frac{9}{5}} \\ \frac{5}{9}(F-32)=C \\ C=\frac{5}{9}(F-32) \end{gathered}[/tex]You can Multiply the bracket (F- 32) by 5/9
[tex]C=\frac{5}{9}F-\frac{160}{9}[/tex]