Cross multiply:
\(c^2 - 4c = 4c+20\)
Simplify into standard form:
\(c^2-8c+20 = 0\)
Complete the square:
\((c - 4)^2 + 4 = 0\)
Subtract 4 from both sides:
\((c-4)^2 = -4\)
Take the square root of both sides:
\(c - 4 = \pm 2i\)
Add 4 to both sides:
\(\color{brown}\boxed{ c = 4 \pm2i}\)