Solve =4x_{1}+6+2x_{1}x_{3}=0

$$= 4 x _ { 1 } + 6 + 2 x _ { 1 } x _ { 3 } = 0$$

Solve for x_1

$$x_{1}=-\frac{3}{x_{3}+2}$$

$$x_{3}\neq -2$$

Steps for Solving Linear Equation

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$4x_{1}+2x_{1}x_{3}=-6$$

Combine all terms containing x_{1}.

$$\left(4+2x_{3}\right)x_{1}=-6$$

The equation is in standard form.

$$\left(2x_{3}+4\right)x_{1}=-6$$

Divide both sides by 4+2x_{3}.

$$\frac{\left(2x_{3}+4\right)x_{1}}{2x_{3}+4}=-\frac{6}{2x_{3}+4}$$

Dividing by 4+2x_{3} undoes the multiplication by 4+2x_{3}.

$$x_{1}=-\frac{6}{2x_{3}+4}$$

Divide -6 by 4+2x_{3}.

$$x_{1}=-\frac{3}{x_{3}+2}$$

Solve for x_3

$$x_{3}=-2-\frac{3}{x_{1}}$$

$$x_{1}\neq 0$$

Steps for Solving Linear Equation

Subtract 4x_{1} from both sides. Anything subtracted from zero gives its negation.

$$6+2x_{1}x_{3}=-4x_{1}$$

Subtract 6 from both sides.

$$2x_{1}x_{3}=-4x_{1}-6$$

Divide both sides by 2x_{1}.

$$\frac{2x_{1}x_{3}}{2x_{1}}=\frac{-4x_{1}-6}{2x_{1}}$$

Dividing by 2x_{1} undoes the multiplication by 2x_{1}.

$$x_{3}=\frac{-4x_{1}-6}{2x_{1}}$$

Divide -4x_{1}-6 by 2x_{1}.

$$x_{3}=-2-\frac{3}{x_{1}}$$