Solve 5g/mw=g/17

$$\frac { 5 g } { m w } = \frac { g } { 17 }$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=0\text{, }&m\neq 0\text{ and }w\neq 0\\g\in \mathrm{C}\text{, }&m=\frac{85}{w}\text{ and }w\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 17mw, the least common multiple of mw,17.

$$17\times 5g=mwg$$

Multiply 17 and 5 to get 85.

$$85g=mwg$$

Subtract mwg from both sides.

$$85g-mwg=0$$

Reorder the terms.

$$-gmw+85g=0$$

Combine all terms containing g.

$$\left(-mw+85\right)g=0$$

The equation is in standard form.

$$\left(85-mw\right)g=0$$

Divide 0 by 85-wm.

$$g=0$$

Solve for g

$$\left\{\begin{matrix}g=0\text{, }&m\neq 0\text{ and }w\neq 0\\g\in \mathrm{R}\text{, }&m=\frac{85}{w}\text{ and }w\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 17mw, the least common multiple of mw,17.

$$17\times 5g=mwg$$

Multiply 17 and 5 to get 85.

$$85g=mwg$$

Subtract mwg from both sides.

$$85g-mwg=0$$

Reorder the terms.

$$-gmw+85g=0$$

Combine all terms containing g.

$$\left(-mw+85\right)g=0$$

The equation is in standard form.

$$\left(85-mw\right)g=0$$

Divide 0 by 85-wm.

$$g=0$$

Solve for m

$$\left\{\begin{matrix}m=\frac{85}{w}\text{, }&w\neq 0\\m\neq 0\text{, }&g=0\text{ and }w\neq 0\end{matrix}\right.$$

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 17mw, the least common multiple of mw,17.

$$17\times 5g=mwg$$

Multiply 17 and 5 to get 85.

$$85g=mwg$$

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

$$mwg=85g$$

The equation is in standard form.

$$gwm=85g$$

Divide both sides by wg.

$$\frac{gwm}{gw}=\frac{85g}{gw}$$

Dividing by wg undoes the multiplication by wg.

$$m=\frac{85g}{gw}$$

Divide 85g by wg.

$$m=\frac{85}{w}$$

Variable m cannot be equal to 0.

$$m=\frac{85}{w}\text{, }m\neq 0$$