Solve f(x)=x+3/5quadg(x)=x*2

$$f ( x ) = \frac { x + 3 } { 5 } \quad g ( x ) = x \cdot 2$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=\frac{10}{x+3}\text{, }&x\neq -3\\g\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$\left(x+3\right)gx=5x\times 2$$

Use the distributive property to multiply x+3 by g.

$$\left(xg+3g\right)x=5x\times 2$$

Use the distributive property to multiply xg+3g by x.

$$gx^{2}+3gx=5x\times 2$$

Multiply 5 and 2 to get 10.

$$gx^{2}+3gx=10x$$

Combine all terms containing g.

$$\left(x^{2}+3x\right)g=10x$$

Divide both sides by x^{2}+3x.

$$\frac{\left(x^{2}+3x\right)g}{x^{2}+3x}=\frac{10x}{x^{2}+3x}$$

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

$$g=\frac{10x}{x^{2}+3x}$$

Divide 10x by x^{2}+3x.

$$g=\frac{10}{x+3}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{10}{x+3}\text{, }&x\neq -3\\g\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$\left(x+3\right)gx=5x\times 2$$

Use the distributive property to multiply x+3 by g.

$$\left(xg+3g\right)x=5x\times 2$$

Use the distributive property to multiply xg+3g by x.

$$gx^{2}+3gx=5x\times 2$$

Multiply 5 and 2 to get 10.

$$gx^{2}+3gx=10x$$

Combine all terms containing g.

$$\left(x^{2}+3x\right)g=10x$$

Divide both sides by x^{2}+3x.

$$\frac{\left(x^{2}+3x\right)g}{x^{2}+3x}=\frac{10x}{x^{2}+3x}$$

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

$$g=\frac{10x}{x^{2}+3x}$$

Divide 10x by x^{2}+3x.

$$g=\frac{10}{x+3}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-3+\frac{10}{g}\text{, }&g\neq 0\end{matrix}\right.$$