Solve A=2pir^2+2pir^2h

$$A = 2 \pi r ^ { 2 } + 2 \pi r ^ { 2 } h$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=-1+\frac{A}{2\pi r^{2}}\text{, }&r\neq 0\\h\in \mathrm{C}\text{, }&A=0\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2\pi r^{2}+2\pi r^{2}h=A$$

Subtract 2\pi r^{2} from both sides.

$$2\pi r^{2}h=A-2\pi r^{2}$$

Divide both sides by 2\pi r^{2}.

$$\frac{2\pi r^{2}h}{2\pi r^{2}}=\frac{A-2\pi r^{2}}{2\pi r^{2}}$$

Dividing by 2\pi r^{2} undoes the multiplication by 2\pi r^{2}.

$$h=\frac{A-2\pi r^{2}}{2\pi r^{2}}$$

Divide A-2\pi r^{2} by 2\pi r^{2}.

$$h=-1+\frac{A}{2\pi r^{2}}$$

Solve for h

$$\left\{\begin{matrix}h=-1+\frac{A}{2\pi r^{2}}\text{, }&r\neq 0\\h\in \mathrm{R}\text{, }&A=0\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2\pi r^{2}+2\pi r^{2}h=A$$

Subtract 2\pi r^{2} from both sides.

$$2\pi r^{2}h=A-2\pi r^{2}$$

Divide both sides by 2\pi r^{2}.

$$\frac{2\pi r^{2}h}{2\pi r^{2}}=\frac{A-2\pi r^{2}}{2\pi r^{2}}$$

Dividing by 2\pi r^{2} undoes the multiplication by 2\pi r^{2}.

$$h=\frac{A-2\pi r^{2}}{2\pi r^{2}}$$

Divide A-2\pi r^{2} by 2\pi r^{2}.

$$h=-1+\frac{A}{2\pi r^{2}}$$

Solve for A

$$A=2\pi \left(h+1\right)r^{2}$$