Solve 5dm^2=(500)cm^2

$$5 dm ^ { 2 } = ( 500 ) cm ^ { 2 }$$

Solve for c

$$\left\{\begin{matrix}\\c=\frac{d}{100}\text{, }&\text{unconditionally}\\c\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$500cm^{2}=5dm^{2}$$

The equation is in standard form.

$$500m^{2}c=5dm^{2}$$

Divide both sides by 500m^{2}.

$$\frac{500m^{2}c}{500m^{2}}=\frac{5dm^{2}}{500m^{2}}$$

Dividing by 500m^{2} undoes the multiplication by 500m^{2}.

$$c=\frac{5dm^{2}}{500m^{2}}$$

Divide 5dm^{2} by 500m^{2}.

$$c=\frac{d}{100}$$

Solve for d

$$\left\{\begin{matrix}\\d=100c\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$5m^{2}d=500cm^{2}$$

Divide both sides by 5m^{2}.

$$\frac{5m^{2}d}{5m^{2}}=\frac{500cm^{2}}{5m^{2}}$$

Dividing by 5m^{2} undoes the multiplication by 5m^{2}.

$$d=\frac{500cm^{2}}{5m^{2}}$$

Divide 500cm^{2} by 5m^{2}.

$$d=100c$$