Solve for c
c=\frac{5\left(f-32\right)}{4}
Solve for f
f=\frac{4\left(c+40\right)}{5}
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4c=5\left(f-32\right)
Multiply both sides of the equation by 20, the least common multiple of 5,4.
4c=5f-160
Use the distributive property to multiply 5 by f-32.
\frac{4c}{4}=\frac{5f-160}{4}
Divide both sides by 4.
c=\frac{5f-160}{4}
Dividing by 4 undoes the multiplication by 4.
c=\frac{5f}{4}-40
Divide -160+5f by 4.
4c=5\left(f-32\right)
Multiply both sides of the equation by 20, the least common multiple of 5,4.
4c=5f-160
Use the distributive property to multiply 5 by f-32.
5f-160=4c
Swap sides so that all variable terms are on the left hand side.
5f=4c+160
Add 160 to both sides.
\frac{5f}{5}=\frac{4c+160}{5}
Divide both sides by 5.
f=\frac{4c+160}{5}
Dividing by 5 undoes the multiplication by 5.
f=\frac{4c}{5}+32
Divide 160+4c by 5.
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