Solve 3x=(n-2)x-(n-3)y

$$3 x = ( n - 2 ) x - ( n - 3 ) y$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{5x-3y}{y-x}\text{, }&x\neq y\\n\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-2 by x.

$$3x=nx-2x-\left(n-3\right)y$$

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

$$3x=nx-2x-\left(ny-3y\right)$$

To find the opposite of ny-3y, find the opposite of each term.

$$3x=nx-2x-ny+3y$$

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

$$nx-2x-ny+3y=3x$$

Add 2x to both sides.

$$nx-ny+3y=3x+2x$$

Combine 3x and 2x to get 5x.

$$nx-ny+3y=5x$$

Subtract 3y from both sides.

$$nx-ny=5x-3y$$

Combine all terms containing n.

$$\left(x-y\right)n=5x-3y$$

Divide both sides by x-y.

$$\frac{\left(x-y\right)n}{x-y}=\frac{5x-3y}{x-y}$$

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

$$n=\frac{5x-3y}{x-y}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{y\left(n-3\right)}{5-n}\text{, }&n\neq 5\\x\in \mathrm{C}\text{, }&y=0\text{ and }n=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-2 by x.

$$3x=nx-2x-\left(n-3\right)y$$

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

$$3x=nx-2x-\left(ny-3y\right)$$

To find the opposite of ny-3y, find the opposite of each term.

$$3x=nx-2x-ny+3y$$

Subtract nx from both sides.

$$3x-nx=-2x-ny+3y$$

Add 2x to both sides.

$$3x-nx+2x=-ny+3y$$

Combine 3x and 2x to get 5x.

$$5x-nx=-ny+3y$$

Combine all terms containing x.

$$\left(5-n\right)x=-ny+3y$$

The equation is in standard form.

$$\left(5-n\right)x=3y-ny$$

Divide both sides by 5-n.

$$\frac{\left(5-n\right)x}{5-n}=\frac{y\left(3-n\right)}{5-n}$$

Dividing by 5-n undoes the multiplication by 5-n.

$$x=\frac{y\left(3-n\right)}{5-n}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{5x-3y}{y-x}\text{, }&x\neq y\\n\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-2 by x.

$$3x=nx-2x-\left(n-3\right)y$$

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

$$3x=nx-2x-\left(ny-3y\right)$$

To find the opposite of ny-3y, find the opposite of each term.

$$3x=nx-2x-ny+3y$$

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

$$nx-2x-ny+3y=3x$$

Add 2x to both sides.

$$nx-ny+3y=3x+2x$$

Combine 3x and 2x to get 5x.

$$nx-ny+3y=5x$$

Subtract 3y from both sides.

$$nx-ny=5x-3y$$

Combine all terms containing n.

$$\left(x-y\right)n=5x-3y$$

Divide both sides by x-y.

$$\frac{\left(x-y\right)n}{x-y}=\frac{5x-3y}{x-y}$$

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

$$n=\frac{5x-3y}{x-y}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{y\left(n-3\right)}{5-n}\text{, }&n\neq 5\\x\in \mathrm{R}\text{, }&y=0\text{ and }n=5\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-2 by x.

$$3x=nx-2x-\left(n-3\right)y$$

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

$$3x=nx-2x-\left(ny-3y\right)$$

To find the opposite of ny-3y, find the opposite of each term.

$$3x=nx-2x-ny+3y$$

Subtract nx from both sides.

$$3x-nx=-2x-ny+3y$$

Add 2x to both sides.

$$3x-nx+2x=-ny+3y$$

Combine 3x and 2x to get 5x.

$$5x-nx=-ny+3y$$

Combine all terms containing x.

$$\left(5-n\right)x=-ny+3y$$

The equation is in standard form.

$$\left(5-n\right)x=3y-ny$$

Divide both sides by 5-n.

$$\frac{\left(5-n\right)x}{5-n}=\frac{y\left(3-n\right)}{5-n}$$

Dividing by 5-n undoes the multiplication by 5-n.

$$x=\frac{y\left(3-n\right)}{5-n}$$