Solve y+2y=(x+dx)

$$y + 2 y = ( x + d x )$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{3y}{x}-1\text{, }&x\neq 0\\d\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine y and 2y to get 3y.

$$3y=x+dx$$

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

$$x+dx=3y$$

Subtract x from both sides.

$$dx=3y-x$$

The equation is in standard form.

$$xd=3y-x$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{3y-x}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{3y-x}{x}$$

Divide 3y-x by x.

$$d=\frac{3y}{x}-1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{3y}{d+1}\text{, }&d\neq -1\\x\in \mathrm{C}\text{, }&y=0\text{ and }d=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine y and 2y to get 3y.

$$3y=x+dx$$

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

$$x+dx=3y$$

Combine all terms containing x.

$$\left(1+d\right)x=3y$$

The equation is in standard form.

$$\left(d+1\right)x=3y$$

Divide both sides by 1+d.

$$\frac{\left(d+1\right)x}{d+1}=\frac{3y}{d+1}$$

Dividing by 1+d undoes the multiplication by 1+d.

$$x=\frac{3y}{d+1}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{3y}{x}-1\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine y and 2y to get 3y.

$$3y=x+dx$$

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

$$x+dx=3y$$

Subtract x from both sides.

$$dx=3y-x$$

The equation is in standard form.

$$xd=3y-x$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{3y-x}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{3y-x}{x}$$

Divide 3y-x by x.

$$d=\frac{3y}{x}-1$$

Solve for x

$$\left\{\begin{matrix}x=\frac{3y}{d+1}\text{, }&d\neq -1\\x\in \mathrm{R}\text{, }&y=0\text{ and }d=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine y and 2y to get 3y.

$$3y=x+dx$$

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

$$x+dx=3y$$

Combine all terms containing x.

$$\left(1+d\right)x=3y$$

The equation is in standard form.

$$\left(d+1\right)x=3y$$

Divide both sides by 1+d.

$$\frac{\left(d+1\right)x}{d+1}=\frac{3y}{d+1}$$

Dividing by 1+d undoes the multiplication by 1+d.

$$x=\frac{3y}{d+1}$$