Solve x^2+3x=bx+2b+x

$$x ^ { 2 } + 3 x = b x + 2 b + x$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=x\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$bx+2b+x=x^{2}+3x$$

Subtract x from both sides.

$$bx+2b=x^{2}+3x-x$$

Combine 3x and -x to get 2x.

$$bx+2b=x^{2}+2x$$

Combine all terms containing b.

$$\left(x+2\right)b=x^{2}+2x$$

Divide both sides by x+2.

$$\frac{\left(x+2\right)b}{x+2}=\frac{x\left(x+2\right)}{x+2}$$

Dividing by x+2 undoes the multiplication by x+2.

$$b=\frac{x\left(x+2\right)}{x+2}$$

Divide x\left(2+x\right) by x+2.

$$b=x$$

Solve for b

$$\left\{\begin{matrix}\\b=x\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$bx+2b+x=x^{2}+3x$$

Subtract x from both sides.

$$bx+2b=x^{2}+3x-x$$

Combine 3x and -x to get 2x.

$$bx+2b=x^{2}+2x$$

Combine all terms containing b.

$$\left(x+2\right)b=x^{2}+2x$$

Divide both sides by x+2.

$$\frac{\left(x+2\right)b}{x+2}=\frac{x\left(x+2\right)}{x+2}$$

Dividing by x+2 undoes the multiplication by x+2.

$$b=\frac{x\left(x+2\right)}{x+2}$$

Divide x\left(2+x\right) by x+2.

$$b=x$$

Solve for x

$$x=b$$

$$x=-2$$