Solve a(x+1)+2y+1=0

$$a(x+1)+2y+1 = 0$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply a by x+1.

$$ax+a+2y+1=0$$

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

$$ax+a+1=-2y$$

Subtract 1 from both sides.

$$ax+a=-2y-1$$

Combine all terms containing a.

$$\left(x+1\right)a=-2y-1$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)a}{x+1}=\frac{-2y-1}{x+1}$$

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

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

Divide -2y-1 by x+1.

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{2y+a+1}{a}\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&y=-\frac{1}{2}\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by x+1.

$$ax+a+2y+1=0$$

Subtract a from both sides. Anything subtracted from zero gives its negation.

$$ax+2y+1=-a$$

Subtract 2y from both sides.

$$ax+1=-a-2y$$

Subtract 1 from both sides.

$$ax=-a-2y-1$$

The equation is in standard form.

$$ax=-2y-a-1$$

Divide both sides by a.

$$\frac{ax}{a}=\frac{-2y-a-1}{a}$$

Dividing by a undoes the multiplication by a.

$$x=\frac{-2y-a-1}{a}$$

Divide -a-2y-1 by a.

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

Solve for a

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

Steps for Solving Linear Equation

Use the distributive property to multiply a by x+1.

$$ax+a+2y+1=0$$

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

$$ax+a+1=-2y$$

Subtract 1 from both sides.

$$ax+a=-2y-1$$

Combine all terms containing a.

$$\left(x+1\right)a=-2y-1$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)a}{x+1}=\frac{-2y-1}{x+1}$$

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

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

Divide -2y-1 by x+1.

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

Solve for x

$$\left\{\begin{matrix}x=-\frac{2y+a+1}{a}\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&y=-\frac{1}{2}\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by x+1.

$$ax+a+2y+1=0$$

Subtract a from both sides. Anything subtracted from zero gives its negation.

$$ax+2y+1=-a$$

Subtract 2y from both sides.

$$ax+1=-a-2y$$

Subtract 1 from both sides.

$$ax=-a-2y-1$$

The equation is in standard form.

$$ax=-2y-a-1$$

Divide both sides by a.

$$\frac{ax}{a}=\frac{-2y-a-1}{a}$$

Dividing by a undoes the multiplication by a.

$$x=\frac{-2y-a-1}{a}$$

Divide -a-2y-1 by a.

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