Solve x(m+7)+y(m-3)=z(m-3)

$$x ( m + 7 ) + y ( m - 3 ) = z ( m - 3 )$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{7x-3y+3z}{x+y-z}\text{, }&x\neq z-y\\m\in \mathrm{R}\text{, }&x=0\text{ and }y=z\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by m+7.

$$xm+7x+y\left(m-3\right)=z\left(m-3\right)$$

Use the distributive property to multiply y by m-3.

$$xm+7x+ym-3y=z\left(m-3\right)$$

Use the distributive property to multiply z by m-3.

$$xm+7x+ym-3y=zm-3z$$

Subtract zm from both sides.

$$xm+7x+ym-3y-zm=-3z$$

Subtract 7x from both sides.

$$xm+ym-3y-zm=-3z-7x$$

Add 3y to both sides.

$$xm+ym-zm=-3z-7x+3y$$

Combine all terms containing m.

$$\left(x+y-z\right)m=-3z-7x+3y$$

The equation is in standard form.

$$\left(x+y-z\right)m=-7x+3y-3z$$

Divide both sides by x+y-z.

$$\frac{\left(x+y-z\right)m}{x+y-z}=\frac{-7x+3y-3z}{x+y-z}$$

Dividing by x+y-z undoes the multiplication by x+y-z.

$$m=\frac{-7x+3y-3z}{x+y-z}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\left(m-3\right)\left(y-z\right)}{m+7}\text{, }&m\neq -7\\x\in \mathrm{R}\text{, }&y=z\text{ and }m=-7\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by m+7.

$$xm+7x+y\left(m-3\right)=z\left(m-3\right)$$

Use the distributive property to multiply y by m-3.

$$xm+7x+ym-3y=z\left(m-3\right)$$

Use the distributive property to multiply z by m-3.

$$xm+7x+ym-3y=zm-3z$$

Subtract ym from both sides.

$$xm+7x-3y=zm-3z-ym$$

Add 3y to both sides.

$$xm+7x=zm-3z-ym+3y$$

Combine all terms containing x.

$$\left(m+7\right)x=zm-3z-ym+3y$$

The equation is in standard form.

$$\left(m+7\right)x=-my+3y+mz-3z$$

Divide both sides by m+7.

$$\frac{\left(m+7\right)x}{m+7}=\frac{\left(m-3\right)\left(z-y\right)}{m+7}$$

Dividing by m+7 undoes the multiplication by m+7.

$$x=\frac{\left(m-3\right)\left(z-y\right)}{m+7}$$