Solve 5m60cm/3m20cm=frac{x_{2}}{5m}

$$\frac { 5 m 60 cm } { 3 m 20 cm } = \frac { x _ { 2 } } { 5 m }$$

Solve for c

$$c\neq 0$$

$$\left(m_{20}x_{2}\neq 0\text{ and }m_{60}=\frac{3m_{20}x_{2}}{25m}\text{ and }m\neq 0\right)\text{ or }\left(x_{2}=0\text{ and }m_{60}=0\text{ and }m\neq 0\text{ and }m_{20}\neq 0\right)$$

Steps for Solving Linear Equation

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15cmm_{20}, the least common multiple of 3m_{20}cm,5m.

$$5\times 5m_{60}cm=3cm_{20}x_{2}$$

Multiply 5 and 5 to get 25.

$$25m_{60}cm=3cm_{20}x_{2}$$

Subtract 3cm_{20}x_{2} from both sides.

$$25m_{60}cm-3cm_{20}x_{2}=0$$

Combine all terms containing c.

$$\left(25m_{60}m-3m_{20}x_{2}\right)c=0$$

The equation is in standard form.

$$\left(25mm_{60}-3m_{20}x_{2}\right)c=0$$

Divide 0 by 25m_{60}m-3x_{2}m_{20}.

$$c=0$$

Variable c cannot be equal to 0.

$$c\in \emptyset$$

Solve for m

$$\left\{\begin{matrix}m=\frac{3m_{20}x_{2}}{25m_{60}}\text{, }&m_{20}\neq 0\text{ and }x_{2}\neq 0\text{ and }m_{60}\neq 0\text{ and }c\neq 0\\m\neq 0\text{, }&x_{2}=0\text{ and }m_{60}=0\text{ and }m_{20}\neq 0\text{ and }c\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15cmm_{20}, the least common multiple of 3m_{20}cm,5m.

$$5\times 5m_{60}cm=3cm_{20}x_{2}$$

Multiply 5 and 5 to get 25.

$$25m_{60}cm=3cm_{20}x_{2}$$

The equation is in standard form.

$$25cm_{60}m=3cm_{20}x_{2}$$

Divide both sides by 25m_{60}c.

$$\frac{25cm_{60}m}{25cm_{60}}=\frac{3cm_{20}x_{2}}{25cm_{60}}$$

Dividing by 25m_{60}c undoes the multiplication by 25m_{60}c.

$$m=\frac{3cm_{20}x_{2}}{25cm_{60}}$$

Divide 3cm_{20}x_{2} by 25m_{60}c.

$$m=\frac{3m_{20}x_{2}}{25m_{60}}$$

Variable m cannot be equal to 0.

$$m=\frac{3m_{20}x_{2}}{25m_{60}}\text{, }m\neq 0$$