Solve 6+xz=1-xL

$$6 + x z = 1 - x L$$

Solve for L

$$L=-z-\frac{5}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$1-xL=6+xz$$

Subtract 1 from both sides.

$$-xL=6+xz-1$$

Subtract 1 from 6 to get 5.

$$-xL=5+xz$$

The equation is in standard form.

$$\left(-x\right)L=xz+5$$

Divide both sides by -x.

$$\frac{\left(-x\right)L}{-x}=\frac{xz+5}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$L=\frac{xz+5}{-x}$$

Divide 5+xz by -x.

$$L=-z-\frac{5}{x}$$

Solve for x

$$x=-\frac{5}{z+L}$$

$$z\neq -L$$

Steps for Solving Linear Equation

Add xL to both sides.

$$6+xz+xL=1$$

Subtract 6 from both sides.

$$xz+xL=1-6$$

Subtract 6 from 1 to get -5.

$$xz+xL=-5$$

Combine all terms containing x.

$$\left(z+L\right)x=-5$$

Divide both sides by L+z.

$$\frac{\left(z+L\right)x}{z+L}=-\frac{5}{z+L}$$

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

$$x=-\frac{5}{z+L}$$