Solve 2x(4y+3z)=1x-2y+1z

$$2 x ( 4 y + 3 z ) = 1 x - 2 y + 1 z$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{2y-z}{8y+6z-1}\text{, }&y\neq -\frac{3z}{4}+\frac{1}{8}\\x\in \mathrm{C}\text{, }&y=\frac{1}{20}\text{ and }z=\frac{1}{10}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$8xy+6xz=1x-2y+1z$$

Subtract 1x from both sides.

$$8xy+6xz-x=-2y+1z$$

Reorder the terms.

$$8xy+6xz-x=-2y+z$$

Combine all terms containing x.

$$\left(8y+6z-1\right)x=-2y+z$$

The equation is in standard form.

$$\left(8y+6z-1\right)x=z-2y$$

Divide both sides by 8y+6z-1.

$$\frac{\left(8y+6z-1\right)x}{8y+6z-1}=\frac{z-2y}{8y+6z-1}$$

Dividing by 8y+6z-1 undoes the multiplication by 8y+6z-1.

$$x=\frac{z-2y}{8y+6z-1}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=-\frac{6xz-x-z}{2\left(4x+1\right)}\text{, }&x\neq -\frac{1}{4}\\y\in \mathrm{C}\text{, }&z=\frac{1}{10}\text{ and }x=-\frac{1}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$8xy+6xz=1x-2y+1z$$

Add 2y to both sides.

$$8xy+6xz+2y=1x+1z$$

Subtract 6xz from both sides.

$$8xy+2y=1x+1z-6xz$$

Reorder the terms.

$$8xy+2y=-6xz+x+z$$

Combine all terms containing y.

$$\left(8x+2\right)y=-6xz+x+z$$

The equation is in standard form.

$$\left(8x+2\right)y=z+x-6xz$$

Divide both sides by 8x+2.

$$\frac{\left(8x+2\right)y}{8x+2}=\frac{z+x-6xz}{8x+2}$$

Dividing by 8x+2 undoes the multiplication by 8x+2.

$$y=\frac{z+x-6xz}{8x+2}$$

Divide -6xz+x+z by 8x+2.

$$y=\frac{z+x-6xz}{2\left(4x+1\right)}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{2y-z}{8y+6z-1}\text{, }&y\neq -\frac{3z}{4}+\frac{1}{8}\\x\in \mathrm{R}\text{, }&y=\frac{1}{20}\text{ and }z=\frac{1}{10}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$8xy+6xz=1x-2y+1z$$

Subtract 1x from both sides.

$$8xy+6xz-x=-2y+1z$$

Reorder the terms.

$$8xy+6xz-x=-2y+z$$

Combine all terms containing x.

$$\left(8y+6z-1\right)x=-2y+z$$

The equation is in standard form.

$$\left(8y+6z-1\right)x=z-2y$$

Divide both sides by 8y+6z-1.

$$\frac{\left(8y+6z-1\right)x}{8y+6z-1}=\frac{z-2y}{8y+6z-1}$$

Dividing by 8y+6z-1 undoes the multiplication by 8y+6z-1.

$$x=\frac{z-2y}{8y+6z-1}$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{6xz-x-z}{2\left(4x+1\right)}\text{, }&x\neq -\frac{1}{4}\\y\in \mathrm{R}\text{, }&z=\frac{1}{10}\text{ and }x=-\frac{1}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$8xy+6xz=1x-2y+1z$$

Add 2y to both sides.

$$8xy+6xz+2y=1x+1z$$

Subtract 6xz from both sides.

$$8xy+2y=1x+1z-6xz$$

Reorder the terms.

$$8xy+2y=-6xz+x+z$$

Combine all terms containing y.

$$\left(8x+2\right)y=-6xz+x+z$$

The equation is in standard form.

$$\left(8x+2\right)y=z+x-6xz$$

Divide both sides by 8x+2.

$$\frac{\left(8x+2\right)y}{8x+2}=\frac{z+x-6xz}{8x+2}$$

Dividing by 8x+2 undoes the multiplication by 8x+2.

$$y=\frac{z+x-6xz}{8x+2}$$

Divide -6xz+x+z by 8x+2.

$$y=\frac{z+x-6xz}{2\left(4x+1\right)}$$