Solve (m-1)x+2y+3=0

$$( m - 1 ) x + 2 y + 3 = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{3+2y-x}{x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&y=-\frac{3}{2}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m-1 by x.

$$mx-x+2y+3=0$$

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

$$mx+2y+3=x$$

Subtract 2y from both sides.

$$mx+3=x-2y$$

Subtract 3 from both sides.

$$mx=x-2y-3$$

The equation is in standard form.

$$xm=x-2y-3$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{x-2y-3}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{x-2y-3}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{2y+3}{m-1}\text{, }&m\neq 1\\x\in \mathrm{C}\text{, }&y=-\frac{3}{2}\text{ and }m=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m-1 by x.

$$mx-x+2y+3=0$$

Subtract 2y from both sides. Anything subtracted from zero gives its negation.

$$mx-x+3=-2y$$

Subtract 3 from both sides.

$$mx-x=-2y-3$$

Combine all terms containing x.

$$\left(m-1\right)x=-2y-3$$

Divide both sides by m-1.

$$\frac{\left(m-1\right)x}{m-1}=\frac{-2y-3}{m-1}$$

Dividing by m-1 undoes the multiplication by m-1.

$$x=\frac{-2y-3}{m-1}$$

Divide -2y-3 by m-1.

$$x=-\frac{2y+3}{m-1}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{3+2y-x}{x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&y=-\frac{3}{2}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m-1 by x.

$$mx-x+2y+3=0$$

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

$$mx+2y+3=x$$

Subtract 2y from both sides.

$$mx+3=x-2y$$

Subtract 3 from both sides.

$$mx=x-2y-3$$

The equation is in standard form.

$$xm=x-2y-3$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{x-2y-3}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{x-2y-3}{x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{2y+3}{m-1}\text{, }&m\neq 1\\x\in \mathrm{R}\text{, }&y=-\frac{3}{2}\text{ and }m=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m-1 by x.

$$mx-x+2y+3=0$$

Subtract 2y from both sides. Anything subtracted from zero gives its negation.

$$mx-x+3=-2y$$

Subtract 3 from both sides.

$$mx-x=-2y-3$$

Combine all terms containing x.

$$\left(m-1\right)x=-2y-3$$

Divide both sides by m-1.

$$\frac{\left(m-1\right)x}{m-1}=\frac{-2y-3}{m-1}$$

Dividing by m-1 undoes the multiplication by m-1.

$$x=\frac{-2y-3}{m-1}$$

Divide -2y-3 by m-1.

$$x=-\frac{2y+3}{m-1}$$