Solve x-(z+1)*x+3z-6=0

$$x-(z+1) \times x+3z-6=0$$

Solve for x

$$x=3-\frac{6}{z}$$

$$z\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply z+1 by x.

$$x-\left(zx+x\right)+3z-6=0$$

To find the opposite of zx+x, find the opposite of each term.

$$x-zx-x+3z-6=0$$

Combine x and -x to get 0.

$$-zx+3z-6=0$$

Subtract 3z from both sides. Anything subtracted from zero gives its negation.

$$-zx-6=-3z$$

Add 6 to both sides.

$$-zx=-3z+6$$

The equation is in standard form.

$$\left(-z\right)x=6-3z$$

Divide both sides by -z.

$$\frac{\left(-z\right)x}{-z}=\frac{6-3z}{-z}$$

Dividing by -z undoes the multiplication by -z.

$$x=\frac{6-3z}{-z}$$

Divide -3z+6 by -z.

$$x=3-\frac{6}{z}$$

Solve for z

$$z=\frac{6}{3-x}$$

$$x\neq 3$$

Steps for Solving Linear Equation

Use the distributive property to multiply z+1 by x.

$$x-\left(zx+x\right)+3z-6=0$$

To find the opposite of zx+x, find the opposite of each term.

$$x-zx-x+3z-6=0$$

Combine x and -x to get 0.

$$-zx+3z-6=0$$

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

$$-zx+3z=6$$

Combine all terms containing z.

$$\left(-x+3\right)z=6$$

The equation is in standard form.

$$\left(3-x\right)z=6$$

Divide both sides by -x+3.

$$\frac{\left(3-x\right)z}{3-x}=\frac{6}{3-x}$$

Dividing by -x+3 undoes the multiplication by -x+3.

$$z=\frac{6}{3-x}$$