Solve 2w(L+h)=2h

$$2 w ( L + h ) = 2 h$$

Solve for L

$$\left\{\begin{matrix}L=-h+\frac{h}{w}\text{, }&w\neq 0\\L\in \mathrm{R}\text{, }&h=0\text{ and }w=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out 2 on both sides.

$$w\left(L+h\right)=h$$

Use the distributive property to multiply w by L+h.

$$wL+wh=h$$

Subtract wh from both sides.

$$wL=h-wh$$

The equation is in standard form.

$$wL=h-hw$$

Divide both sides by w.

$$\frac{wL}{w}=\frac{h-hw}{w}$$

Dividing by w undoes the multiplication by w.

$$L=\frac{h-hw}{w}$$

Divide h-hw by w.

$$L=-h+\frac{h}{w}$$

Solve for h

$$\left\{\begin{matrix}h=-\frac{Lw}{w-1}\text{, }&w\neq 1\\h\in \mathrm{R}\text{, }&L=0\text{ and }w=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out 2 on both sides.

$$w\left(L+h\right)=h$$

Use the distributive property to multiply w by L+h.

$$wL+wh=h$$

Subtract h from both sides.

$$wL+wh-h=0$$

Subtract wL from both sides. Anything subtracted from zero gives its negation.

$$wh-h=-wL$$

Reorder the terms.

$$hw-h=-Lw$$

Combine all terms containing h.

$$\left(w-1\right)h=-Lw$$

Divide both sides by w-1.

$$\frac{\left(w-1\right)h}{w-1}=-\frac{Lw}{w-1}$$

Dividing by w-1 undoes the multiplication by w-1.

$$h=-\frac{Lw}{w-1}$$