Solve ac^2=AB^2

$$a c ^ { 2 } = A B ^ { 2 }$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\left(\frac{c}{B}\right)^{2}a\text{, }&B\neq 0\\A\in \mathrm{C}\text{, }&\left(a=0\text{ or }c=0\right)\text{ and }B=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$AB^{2}=ac^{2}$$

The equation is in standard form.

$$B^{2}A=ac^{2}$$

Divide both sides by B^{2}.

$$\frac{B^{2}A}{B^{2}}=\frac{ac^{2}}{B^{2}}$$

Dividing by B^{2} undoes the multiplication by B^{2}.

$$A=\frac{ac^{2}}{B^{2}}$$

Solve for A

$$\left\{\begin{matrix}A=\left(\frac{c}{B}\right)^{2}a\text{, }&B\neq 0\\A\in \mathrm{R}\text{, }&\left(a=0\text{ or }c=0\right)\text{ and }B=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$AB^{2}=ac^{2}$$

The equation is in standard form.

$$B^{2}A=ac^{2}$$

Divide both sides by B^{2}.

$$\frac{B^{2}A}{B^{2}}=\frac{ac^{2}}{B^{2}}$$

Dividing by B^{2} undoes the multiplication by B^{2}.

$$A=\frac{ac^{2}}{B^{2}}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=-A^{-\frac{1}{2}}\sqrt{a}c\text{; }B=A^{-\frac{1}{2}}\sqrt{a}c\text{, }&A\neq 0\\B\in \mathrm{C}\text{, }&\left(a=0\text{ or }c=0\right)\text{ and }A=0\end{matrix}\right.$$

Solve for B

$$\left\{\begin{matrix}B=\sqrt{\frac{a}{A}}c\text{; }B=-\sqrt{\frac{a}{A}}c\text{, }&\left(a\geq 0\text{ and }A>0\right)\text{ or }\left(a\leq 0\text{ and }A<0\right)\\B=0\text{, }&c=0\text{ and }A\neq 0\\B\in \mathrm{R}\text{, }&\left(a=0\text{ or }c=0\right)\text{ and }A=0\end{matrix}\right.$$