Solve 4x=ay-zx

$$4 x = a y - z x$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x\left(z+4\right)}{y}\text{, }&y\neq 0\\a\in \mathrm{R}\text{, }&\left(x=0\text{ or }z=-4\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ay-zx=4x$$

Add zx to both sides.

$$ay=4x+zx$$

The equation is in standard form.

$$ya=xz+4x$$

Divide both sides by y.

$$\frac{ya}{y}=\frac{x\left(z+4\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$a=\frac{x\left(z+4\right)}{y}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{ay}{z+4}\text{, }&z\neq -4\\x\in \mathrm{R}\text{, }&\left(a=0\text{ or }y=0\right)\text{ and }z=-4\end{matrix}\right.$$

Steps for Solving Linear Equation

Add zx to both sides.

$$4x+zx=ay$$

Combine all terms containing x.

$$\left(4+z\right)x=ay$$

The equation is in standard form.

$$\left(z+4\right)x=ay$$

Divide both sides by 4+z.

$$\frac{\left(z+4\right)x}{z+4}=\frac{ay}{z+4}$$

Dividing by 4+z undoes the multiplication by 4+z.

$$x=\frac{ay}{z+4}$$