Solve A=7(8x-6)-(-5p+4)^I

$$A = 7 ( 8 x - 6 ) - ( - 5 p + 4 ) ^ { I }$$

Solve for A (complex solution)

$$A=-\left(\left(4-5p\right)^{I}-56x+42\right)$$

Solve for I (complex solution)

$$\left\{\begin{matrix}I=\frac{2i\pi n_{1}}{\ln(4-5p)}+\log_{4-5p}\left(-\left(42+A-56x\right)\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&A\neq 56x-42\text{ and }p\neq \frac{3}{5}\text{ and }p\neq \frac{4}{5}\\I\in \mathrm{C}\text{, }&\left(p=\frac{4}{5}\text{ and }A=56x-42\right)\text{ or }\left(p=\frac{3}{5}\text{ and }A=56x-43\right)\end{matrix}\right.$$

Solve for A

$$A=-\left(\left(4-5p\right)^{I}-56x+42\right)$$

$$\left(p>\frac{4}{5}\text{ and }Denominator(I)\text{bmod}2=1\right)\text{ or }\left(p=\frac{4}{5}\text{ and }I>0\right)\text{ or }p<\frac{4}{5}$$

Solve for I

$$\left\{\begin{matrix}I=\log_{4-5p}\left(56x-A-42\right)\text{, }&A<56x-42\text{ and }p\neq \frac{3}{5}\text{ and }p<\frac{4}{5}\\I\in \mathrm{R}\text{, }&\left(p=\frac{3}{5}\text{ and }A=56x-43\right)\text{ or }\left(p=1\text{ and }A=56x-41\text{ and }Denominator(I)\text{bmod}2=1\text{ and }Numerator(I)\text{bmod}2=1\right)\\I>0\text{, }&p=\frac{4}{5}\text{ and }A=56x-42\end{matrix}\right.$$