Solve 24c^2d/9p^2-25*5-3/12cd^3=8/3

$$\frac { 24 c ^ { 2 } d } { 9 p ^ { 2 } - 25 } \cdot \frac { 5 - 3 } { 12 c d ^ { 3 } } = \frac { 8 } { 3 }$$

Solve for c (complex solution)

$$c=\frac{2d^{2}\left(9p^{2}-25\right)}{3}$$

$$d\neq 0\text{ and }p\neq -\frac{5}{3}\text{ and }p\neq \frac{5}{3}$$

Solve for d (complex solution)

$$d=-\frac{i\left(25-9p^{2}\right)^{-\frac{1}{2}}\sqrt{6c}}{2}$$

$$d=\frac{i\left(25-9p^{2}\right)^{-\frac{1}{2}}\sqrt{6c}}{2}\text{, }c\neq 0\text{ and }p\neq -\frac{5}{3}\text{ and }p\neq \frac{5}{3}$$

Solve for c

$$c=\frac{2d^{2}\left(9p^{2}-25\right)}{3}$$

$$d\neq 0\text{ and }|p|\neq \frac{5}{3}$$

Solve for d

$$d=\frac{\sqrt{-\frac{6c}{25-9p^{2}}}}{2}$$

$$d=-\frac{\sqrt{-\frac{6c}{25-9p^{2}}}}{2}\text{, }\left(|p|>\frac{5}{3}\text{ and }c>0\right)\text{ or }\left(|p|<\frac{5}{3}\text{ and }c<0\right)$$