Solve 1dm^3=quad1,0quadmL

$$1 dm ^ { 3 } = \quad 1,0 \quad mL$$

Solve for L

$$\left\{\begin{matrix}\\L=dm^{2}\text{, }&\text{unconditionally}\\L\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out 1 on both sides.

$$dm^{3}=mL$$

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

$$mL=dm^{3}$$

Divide both sides by m.

$$\frac{mL}{m}=\frac{dm^{3}}{m}$$

Dividing by m undoes the multiplication by m.

$$L=\frac{dm^{3}}{m}$$

Divide dm^{3} by m.

$$L=dm^{2}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{L}{m^{2}}\text{, }&m\neq 0\\d\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out 1 on both sides.

$$dm^{3}=mL$$

The equation is in standard form.

$$m^{3}d=Lm$$

Divide both sides by m^{3}.

$$\frac{m^{3}d}{m^{3}}=\frac{Lm}{m^{3}}$$

Dividing by m^{3} undoes the multiplication by m^{3}.

$$d=\frac{Lm}{m^{3}}$$

Divide mL by m^{3}.

$$d=\frac{L}{m^{2}}$$