#### Answer

The equation has two solutions, -10 and 10.

#### Work Step by Step

$\frac{4}{c+4}=\frac{c}{c+25}$
$4(c+25)=c(c+4)$ (Cross Products Property)
$4c+100=c^2+4c$
$c^2=100$
$c=10$ or $c=-10$
Check:
$4/(10+4)=2/7;10/(10+25)=2/7$
$4/(-10+4)=-2/3;-10/(-10+25)=-2/3$
The equation has two solutions, -10 and 10.