Solve -13x+12xy+y+z-8xz=4x(3y-2z-3)+y

$$-13x+12xy+y+z-8xz=4x(3y-2z-3)+y$$

Solve for x

$$x=z$$

Solution Steps

Use the distributive property to multiply 4x by 3y-2z-3.

$$-13x+12xy+y+z-8xz=12xy-8xz-12x+y$$

Subtract 12xy from both sides.

$$-13x+12xy+y+z-8xz-12xy=-8xz-12x+y$$

Combine 12xy and -12xy to get 0.

$$-13x+y+z-8xz=-8xz-12x+y$$

Add 8xz to both sides.

$$-13x+y+z-8xz+8xz=-12x+y$$

Combine -8xz and 8xz to get 0.

$$-13x+y+z=-12x+y$$

Add 12x to both sides.

$$-13x+y+z+12x=y$$

Combine -13x and 12x to get -x.

$$-x+y+z=y$$

Subtract y from both sides.

$$-x+z=y-y$$

Combine y and -y to get 0.

$$-x+z=0$$

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

$$-x=-z$$

Cancel out -1 on both sides.

$$x=z$$

Solve for y (complex solution)

$$y\in \mathrm{C}$$

$$x=z$$

Solve for y

$$y\in \mathrm{R}$$

$$x=z$$