Solve 3x2y(x+y)4x/x+2-2yz=4

$$\frac { 3 x 2 y ( x + y ) 4 x } { x + 2 - 2 y } z = 4$$

Solve for x_2

$$x_{2}=-\frac{-x+2y-2}{3xyz\left(x+y\right)}$$

$$z\neq 0\text{ and }x\neq 0\text{ and }y\neq -x\text{ and }y\neq 0\text{ and }y\neq \frac{x}{2}+1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2y+2.

$$3x_{2}y\left(x+y\right)\times 4xz=4\left(x-2y+2\right)$$

Multiply 3 and 4 to get 12.

$$12x_{2}y\left(x+y\right)xz=4\left(x-2y+2\right)$$

Use the distributive property to multiply 12x_{2}y by x+y.

$$\left(12x_{2}yx+12x_{2}y^{2}\right)xz=4\left(x-2y+2\right)$$

Use the distributive property to multiply 12x_{2}yx+12x_{2}y^{2} by x.

$$\left(12x_{2}yx^{2}+12x_{2}y^{2}x\right)z=4\left(x-2y+2\right)$$

Use the distributive property to multiply 12x_{2}yx^{2}+12x_{2}y^{2}x by z.

$$12x_{2}yx^{2}z+12x_{2}y^{2}xz=4\left(x-2y+2\right)$$

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

$$12x_{2}yx^{2}z+12x_{2}y^{2}xz=4x-8y+8$$

Combine all terms containing x_{2}.

$$\left(12yx^{2}z+12y^{2}xz\right)x_{2}=4x-8y+8$$

The equation is in standard form.

$$\left(12xzy^{2}+12yzx^{2}\right)x_{2}=4x-8y+8$$

Divide both sides by 12yx^{2}z+12y^{2}xz.

$$\frac{\left(12xzy^{2}+12yzx^{2}\right)x_{2}}{12xzy^{2}+12yzx^{2}}=\frac{4x-8y+8}{12xzy^{2}+12yzx^{2}}$$

Dividing by 12yx^{2}z+12y^{2}xz undoes the multiplication by 12yx^{2}z+12y^{2}xz.

$$x_{2}=\frac{4x-8y+8}{12xzy^{2}+12yzx^{2}}$$

Divide 8+4x-8y by 12yx^{2}z+12y^{2}xz.

$$x_{2}=\frac{x-2y+2}{3xyz\left(x+y\right)}$$