Solve ax^3+bx+cx+d=0

$$a x ^ { 3 } + b x + c x + d = 0$$

Solve for a

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

Steps for Solving Linear Equation

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

$$ax^{3}+cx+d=-bx$$

Subtract cx from both sides.

$$ax^{3}+d=-bx-cx$$

Subtract d from both sides.

$$ax^{3}=-bx-cx-d$$

The equation is in standard form.

$$x^{3}a=-bx-cx-d$$

Divide both sides by x^{3}.

$$\frac{x^{3}a}{x^{3}}=\frac{-bx-cx-d}{x^{3}}$$

Dividing by x^{3} undoes the multiplication by x^{3}.

$$a=\frac{-bx-cx-d}{x^{3}}$$

Divide -bx-cx-d by x^{3}.

$$a=-\frac{bx+cx+d}{x^{3}}$$

Solve for b

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

Steps for Solving Linear Equation

Subtract ax^{3} from both sides. Anything subtracted from zero gives its negation.

$$bx+cx+d=-ax^{3}$$

Subtract cx from both sides.

$$bx+d=-ax^{3}-cx$$

Subtract d from both sides.

$$bx=-ax^{3}-cx-d$$

The equation is in standard form.

$$xb=-ax^{3}-cx-d$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{-ax^{3}-cx-d}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{-ax^{3}-cx-d}{x}$$

Divide -ax^{3}-cx-d by x.

$$b=-ax^{2}-c-\frac{d}{x}$$