Solve dx+bx+c=0

$$d x + b x + c = 0$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{dx+c}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$bx+c=-dx$$

Subtract c from both sides.

$$bx=-dx-c$$

The equation is in standard form.

$$xb=-dx-c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{-dx-c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{-dx-c}{x}$$

Divide -dx-c by x.

$$b=-d-\frac{c}{x}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{dx+c}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$bx+c=-dx$$

Subtract c from both sides.

$$bx=-dx-c$$

The equation is in standard form.

$$xb=-dx-c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{-dx-c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{-dx-c}{x}$$

Divide -dx-c by x.

$$b=-d-\frac{c}{x}$$

Solve for c

$$c=-x\left(b+d\right)$$