Solve -3(x-1)+9(y-1)+6(z+1)=0

$$- 3 ( x - 1 ) + 9 ( y - 1 ) + 6 ( z + 1 ) = 0$$

Solve for x

$$x=3y+2z$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by x-1.

$$-3x+3+9\left(y-1\right)+6\left(z+1\right)=0$$

Use the distributive property to multiply 9 by y-1.

$$-3x+3+9y-9+6\left(z+1\right)=0$$

Subtract 9 from 3 to get -6.

$$-3x-6+9y+6\left(z+1\right)=0$$

Use the distributive property to multiply 6 by z+1.

$$-3x-6+9y+6z+6=0$$

Add -6 and 6 to get 0.

$$-3x+9y+6z=0$$

Subtract 9y from both sides. Anything subtracted from zero gives its negation.

$$-3x+6z=-9y$$

Subtract 6z from both sides.

$$-3x=-9y-6z$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{-9y-6z}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{-9y-6z}{-3}$$

Divide -9y-6z by -3.

$$x=3y+2z$$

Solve for y

$$y=\frac{x-2z}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by x-1.

$$-3x+3+9\left(y-1\right)+6\left(z+1\right)=0$$

Use the distributive property to multiply 9 by y-1.

$$-3x+3+9y-9+6\left(z+1\right)=0$$

Subtract 9 from 3 to get -6.

$$-3x-6+9y+6\left(z+1\right)=0$$

Use the distributive property to multiply 6 by z+1.

$$-3x-6+9y+6z+6=0$$

Add -6 and 6 to get 0.

$$-3x+9y+6z=0$$

Add 3x to both sides. Anything plus zero gives itself.

$$9y+6z=3x$$

Subtract 6z from both sides.

$$9y=3x-6z$$

Divide both sides by 9.

$$\frac{9y}{9}=\frac{3x-6z}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$y=\frac{3x-6z}{9}$$

Divide 3x-6z by 9.

$$y=\frac{x-2z}{3}$$