Solve yx-5zx-52x-6z-74=0

$$yx-5zx-52x-6z-74=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{2\left(3z+37\right)}{y-5z-52}\text{, }&y\neq 5z+52\\x\in \mathrm{C}\text{, }&z=-\frac{37}{3}\text{ and }y=-\frac{29}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 6z to both sides. Anything plus zero gives itself.

$$yx-5zx-52x-74=6z$$

Add 74 to both sides.

$$yx-5zx-52x=6z+74$$

Combine all terms containing x.

$$\left(y-5z-52\right)x=6z+74$$

Divide both sides by y-5z-52.

$$\frac{\left(y-5z-52\right)x}{y-5z-52}=\frac{6z+74}{y-5z-52}$$

Dividing by y-5z-52 undoes the multiplication by y-5z-52.

$$x=\frac{6z+74}{y-5z-52}$$

Divide 6z+74 by y-5z-52.

$$x=\frac{2\left(3z+37\right)}{y-5z-52}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{5xz+52x+6z+74}{x}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&z=-\frac{37}{3}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 5zx to both sides. Anything plus zero gives itself.

$$yx-52x-6z-74=5zx$$

Add 52x to both sides.

$$yx-6z-74=5zx+52x$$

Add 6z to both sides.

$$yx-74=5zx+52x+6z$$

Add 74 to both sides.

$$yx=5zx+52x+6z+74$$

The equation is in standard form.

$$xy=5xz+52x+6z+74$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{5xz+52x+6z+74}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{5xz+52x+6z+74}{x}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2\left(3z+37\right)}{y-5z-52}\text{, }&y\neq 5z+52\\x\in \mathrm{R}\text{, }&z=-\frac{37}{3}\text{ and }y=-\frac{29}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 6z to both sides. Anything plus zero gives itself.

$$yx-5zx-52x-74=6z$$

Add 74 to both sides.

$$yx-5zx-52x=6z+74$$

Combine all terms containing x.

$$\left(y-5z-52\right)x=6z+74$$

Divide both sides by y-5z-52.

$$\frac{\left(y-5z-52\right)x}{y-5z-52}=\frac{6z+74}{y-5z-52}$$

Dividing by y-5z-52 undoes the multiplication by y-5z-52.

$$x=\frac{6z+74}{y-5z-52}$$

Divide 6z+74 by y-5z-52.

$$x=\frac{2\left(3z+37\right)}{y-5z-52}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{5xz+52x+6z+74}{x}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&z=-\frac{37}{3}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 5zx to both sides. Anything plus zero gives itself.

$$yx-52x-6z-74=5zx$$

Add 52x to both sides.

$$yx-6z-74=5zx+52x$$

Add 6z to both sides.

$$yx-74=5zx+52x+6z$$

Add 74 to both sides.

$$yx=5zx+52x+6z+74$$

The equation is in standard form.

$$xy=5xz+52x+6z+74$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{5xz+52x+6z+74}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{5xz+52x+6z+74}{x}$$