Solve f(x)dx=x^3/3-x^2/2-2x

$$f ( x ) d x = \frac { x ^ { 3 } } { 3 } - \frac { x ^ { 2 } } { 2 } - 2 x$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=-\frac{12+3x-2x^{2}}{6fx}\text{, }&x\neq 0\text{ and }f\neq 0\\d\in \mathrm{C}\text{, }&x=0\text{ or }\left(x=\frac{3-\sqrt{105}}{4}\text{ and }f=0\right)\text{ or }\left(x=\frac{\sqrt{105}+3}{4}\text{ and }f=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$6fxdx=2x^{3}-3x^{2}-12x$$

Multiply x and x to get x^{2}.

$$6fx^{2}d=2x^{3}-3x^{2}-12x$$

Divide both sides by 6fx^{2}.

$$\frac{6fx^{2}d}{6fx^{2}}=\frac{x\left(2x^{2}-3x-12\right)}{6fx^{2}}$$

Dividing by 6fx^{2} undoes the multiplication by 6fx^{2}.

$$d=\frac{x\left(2x^{2}-3x-12\right)}{6fx^{2}}$$

Divide x\left(2x^{2}-3x-12\right) by 6fx^{2}.

$$d=\frac{2x^{2}-3x-12}{6fx}$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{12+3x-2x^{2}}{6dx}\text{, }&x\neq 0\text{ and }d\neq 0\\f\in \mathrm{C}\text{, }&x=0\text{ or }\left(x=\frac{3-\sqrt{105}}{4}\text{ and }d=0\right)\text{ or }\left(x=\frac{\sqrt{105}+3}{4}\text{ and }d=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$6fxdx=2x^{3}-3x^{2}-12x$$

Multiply x and x to get x^{2}.

$$6fx^{2}d=2x^{3}-3x^{2}-12x$$

The equation is in standard form.

$$6dx^{2}f=2x^{3}-3x^{2}-12x$$

Divide both sides by 6x^{2}d.

$$\frac{6dx^{2}f}{6dx^{2}}=\frac{x\left(2x^{2}-3x-12\right)}{6dx^{2}}$$

Dividing by 6x^{2}d undoes the multiplication by 6x^{2}d.

$$f=\frac{x\left(2x^{2}-3x-12\right)}{6dx^{2}}$$

Divide x\left(2x^{2}-3x-12\right) by 6x^{2}d.

$$f=\frac{2x^{2}-3x-12}{6dx}$$

Solve for d

$$\left\{\begin{matrix}d=-\frac{12+3x-2x^{2}}{6fx}\text{, }&x\neq 0\text{ and }f\neq 0\\d\in \mathrm{R}\text{, }&x=0\text{ or }\left(x=\frac{3-\sqrt{105}}{4}\text{ and }f=0\right)\text{ or }\left(x=\frac{\sqrt{105}+3}{4}\text{ and }f=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$6fxdx=2x^{3}-3x^{2}-12x$$

Multiply x and x to get x^{2}.

$$6fx^{2}d=2x^{3}-3x^{2}-12x$$

Divide both sides by 6fx^{2}.

$$\frac{6fx^{2}d}{6fx^{2}}=\frac{x\left(2x^{2}-3x-12\right)}{6fx^{2}}$$

Dividing by 6fx^{2} undoes the multiplication by 6fx^{2}.

$$d=\frac{x\left(2x^{2}-3x-12\right)}{6fx^{2}}$$

Divide x\left(2x^{2}-3x-12\right) by 6fx^{2}.

$$d=\frac{2x^{2}-3x-12}{6fx}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{12+3x-2x^{2}}{6dx}\text{, }&x\neq 0\text{ and }d\neq 0\\f\in \mathrm{R}\text{, }&x=0\text{ or }\left(x=\frac{3-\sqrt{105}}{4}\text{ and }d=0\right)\text{ or }\left(x=\frac{\sqrt{105}+3}{4}\text{ and }d=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$6fxdx=2x^{3}-3x^{2}-12x$$

Multiply x and x to get x^{2}.

$$6fx^{2}d=2x^{3}-3x^{2}-12x$$

The equation is in standard form.

$$6dx^{2}f=2x^{3}-3x^{2}-12x$$

Divide both sides by 6x^{2}d.

$$\frac{6dx^{2}f}{6dx^{2}}=\frac{x\left(2x^{2}-3x-12\right)}{6dx^{2}}$$

Dividing by 6x^{2}d undoes the multiplication by 6x^{2}d.

$$f=\frac{x\left(2x^{2}-3x-12\right)}{6dx^{2}}$$

Divide x\left(2x^{2}-3x-12\right) by 6x^{2}d.

$$f=\frac{2x^{2}-3x-12}{6dx}$$