Solve a*x^3+b*x^2+cx+d=0

$$a \cdot x ^ { 3 } + b \cdot x ^ { 2 } + c x + d = 0$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bx^{2}+cx+d}{x^{3}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&d=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx^{2} from both sides. Anything subtracted from zero gives its negation.

$$ax^{3}+cx+d=-bx^{2}$$

Subtract cx from both sides.

$$ax^{3}+d=-bx^{2}-cx$$

Subtract d from both sides.

$$ax^{3}=-bx^{2}-cx-d$$

The equation is in standard form.

$$x^{3}a=-bx^{2}-cx-d$$

Divide both sides by x^{3}.

$$\frac{x^{3}a}{x^{3}}=\frac{-bx^{2}-cx-d}{x^{3}}$$

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

$$a=\frac{-bx^{2}-cx-d}{x^{3}}$$

Divide -bx^{2}-cx-d by x^{3}.

$$a=-\frac{bx^{2}+cx+d}{x^{3}}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{ax^{3}+cx+d}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&d=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$bx^{2}+cx+d=-ax^{3}$$

Subtract cx from both sides.

$$bx^{2}+d=-ax^{3}-cx$$

Subtract d from both sides.

$$bx^{2}=-ax^{3}-cx-d$$

The equation is in standard form.

$$x^{2}b=-ax^{3}-cx-d$$

Divide both sides by x^{2}.

$$\frac{x^{2}b}{x^{2}}=\frac{-ax^{3}-cx-d}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$b=\frac{-ax^{3}-cx-d}{x^{2}}$$

Divide -ax^{3}-cx-d by x^{2}.

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