Solve mx+my+mx-my-15x-7y=0

$$m x + m y + m x - m y - 15 x - 7 y = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{7y}{2x}+\frac{15}{2}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine mx and mx to get 2mx.

$$2mx+my-my-15x-7y=0$$

Combine my and -my to get 0.

$$2mx-15x-7y=0$$

Add 15x to both sides. Anything plus zero gives itself.

$$2mx-7y=15x$$

Add 7y to both sides.

$$2mx=15x+7y$$

The equation is in standard form.

$$2xm=15x+7y$$

Divide both sides by 2x.

$$\frac{2xm}{2x}=\frac{15x+7y}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$m=\frac{15x+7y}{2x}$$

Divide 15x+7y by 2x.

$$m=\frac{7y}{2x}+\frac{15}{2}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{7y}{2m-15}\text{, }&m\neq \frac{15}{2}\\x\in \mathrm{C}\text{, }&y=0\text{ and }m=\frac{15}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine mx and mx to get 2mx.

$$2mx+my-my-15x-7y=0$$

Combine my and -my to get 0.

$$2mx-15x-7y=0$$

Add 7y to both sides. Anything plus zero gives itself.

$$2mx-15x=7y$$

Combine all terms containing x.

$$\left(2m-15\right)x=7y$$

Divide both sides by 2m-15.

$$\frac{\left(2m-15\right)x}{2m-15}=\frac{7y}{2m-15}$$

Dividing by 2m-15 undoes the multiplication by 2m-15.

$$x=\frac{7y}{2m-15}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{7y}{2x}+\frac{15}{2}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine mx and mx to get 2mx.

$$2mx+my-my-15x-7y=0$$

Combine my and -my to get 0.

$$2mx-15x-7y=0$$

Add 15x to both sides. Anything plus zero gives itself.

$$2mx-7y=15x$$

Add 7y to both sides.

$$2mx=15x+7y$$

The equation is in standard form.

$$2xm=15x+7y$$

Divide both sides by 2x.

$$\frac{2xm}{2x}=\frac{15x+7y}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$m=\frac{15x+7y}{2x}$$

Divide 15x+7y by 2x.

$$m=\frac{7y}{2x}+\frac{15}{2}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{7y}{2m-15}\text{, }&m\neq \frac{15}{2}\\x\in \mathrm{R}\text{, }&y=0\text{ and }m=\frac{15}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine mx and mx to get 2mx.

$$2mx+my-my-15x-7y=0$$

Combine my and -my to get 0.

$$2mx-15x-7y=0$$

Add 7y to both sides. Anything plus zero gives itself.

$$2mx-15x=7y$$

Combine all terms containing x.

$$\left(2m-15\right)x=7y$$

Divide both sides by 2m-15.

$$\frac{\left(2m-15\right)x}{2m-15}=\frac{7y}{2m-15}$$

Dividing by 2m-15 undoes the multiplication by 2m-15.

$$x=\frac{7y}{2m-15}$$