Solve F(x)=3xdx

$$F ( x ) = 3 x d x$$

Solve for F (complex solution)

$$\left\{\begin{matrix}\\F=3dx\text{, }&\text{unconditionally}\\F\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Fx=3x^{2}d$$

The equation is in standard form.

$$xF=3dx^{2}$$

Divide both sides by x.

$$\frac{xF}{x}=\frac{3dx^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$F=\frac{3dx^{2}}{x}$$

Divide 3x^{2}d by x.

$$F=3dx$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{F}{3x}\text{, }&x\neq 0\\d\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Fx=3x^{2}d$$

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

$$3x^{2}d=Fx$$

Divide both sides by 3x^{2}.

$$\frac{3x^{2}d}{3x^{2}}=\frac{Fx}{3x^{2}}$$

Dividing by 3x^{2} undoes the multiplication by 3x^{2}.

$$d=\frac{Fx}{3x^{2}}$$

Divide Fx by 3x^{2}.

$$d=\frac{F}{3x}$$

Solve for F

$$\left\{\begin{matrix}\\F=3dx\text{, }&\text{unconditionally}\\F\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Fx=3x^{2}d$$

The equation is in standard form.

$$xF=3dx^{2}$$

Divide both sides by x.

$$\frac{xF}{x}=\frac{3dx^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$F=\frac{3dx^{2}}{x}$$

Divide 3x^{2}d by x.

$$F=3dx$$

Solve for d

$$\left\{\begin{matrix}d=\frac{F}{3x}\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$Fx=3x^{2}d$$

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

$$3x^{2}d=Fx$$

Divide both sides by 3x^{2}.

$$\frac{3x^{2}d}{3x^{2}}=\frac{Fx}{3x^{2}}$$

Dividing by 3x^{2} undoes the multiplication by 3x^{2}.

$$d=\frac{Fx}{3x^{2}}$$

Divide Fx by 3x^{2}.

$$d=\frac{F}{3x}$$