Solve x*(3y+1)-3x(x+4)=0

$$x \times ( 3 y + 1 ) - 3 x ( x + 4 ) = 0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=x+\frac{11}{3}\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 3y+1.

$$3xy+x-3x\left(x+4\right)=0$$

Add 3x\left(x+4\right) to both sides.

$$3xy+x=0+3x\left(x+4\right)$$

Use the distributive property to multiply 3x by x+4.

$$3xy+x=0+3x^{2}+12x$$

Anything plus zero gives itself.

$$3xy+x=3x^{2}+12x$$

Subtract x from both sides.

$$3xy=3x^{2}+12x-x$$

Combine 12x and -x to get 11x.

$$3xy=3x^{2}+11x$$

Divide both sides by 3x.

$$\frac{3xy}{3x}=\frac{x\left(3x+11\right)}{3x}$$

Dividing by 3x undoes the multiplication by 3x.

$$y=\frac{x\left(3x+11\right)}{3x}$$

Divide x\left(11+3x\right) by 3x.

$$y=x+\frac{11}{3}$$

Solve for y

$$\left\{\begin{matrix}\\y=x+\frac{11}{3}\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 3y+1.

$$3xy+x-3x\left(x+4\right)=0$$

Add 3x\left(x+4\right) to both sides.

$$3xy+x=0+3x\left(x+4\right)$$

Use the distributive property to multiply 3x by x+4.

$$3xy+x=0+3x^{2}+12x$$

Anything plus zero gives itself.

$$3xy+x=3x^{2}+12x$$

Subtract x from both sides.

$$3xy=3x^{2}+12x-x$$

Combine 12x and -x to get 11x.

$$3xy=3x^{2}+11x$$

Divide both sides by 3x.

$$\frac{3xy}{3x}=\frac{x\left(3x+11\right)}{3x}$$

Dividing by 3x undoes the multiplication by 3x.

$$y=\frac{x\left(3x+11\right)}{3x}$$

Divide x\left(11+3x\right) by 3x.

$$y=x+\frac{11}{3}$$

Solve for x

$$x = -\frac{11}{3} = -3\frac{2}{3} = -3.6666666666666665$$

$$x=0$$