Solve (2-y)*(z+y)-(6y-y^2)=4

$$( 2 - y ) \cdot ( z + y ) - ( 6 y - y ^ { 2 } ) = 4$$

Solve for y

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

$$z\neq -4$$

Steps for Solving Linear Equation

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

$$2z+2y-yz-y^{2}-\left(6y-y^{2}\right)=4$$

To find the opposite of 6y-y^{2}, find the opposite of each term.

$$2z+2y-yz-y^{2}-6y+y^{2}=4$$

Combine 2y and -6y to get -4y.

$$2z-4y-yz-y^{2}+y^{2}=4$$

Combine -y^{2} and y^{2} to get 0.

$$2z-4y-yz=4$$

Subtract 2z from both sides.

$$-4y-yz=4-2z$$

Combine all terms containing y.

$$\left(-4-z\right)y=4-2z$$

The equation is in standard form.

$$\left(-z-4\right)y=4-2z$$

Divide both sides by -z-4.

$$\frac{\left(-z-4\right)y}{-z-4}=\frac{4-2z}{-z-4}$$

Dividing by -z-4 undoes the multiplication by -z-4.

$$y=\frac{4-2z}{-z-4}$$

Divide 4-2z by -z-4.

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

Solve for z

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

$$y\neq 2$$

Steps for Solving Linear Equation

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

$$2z+2y-yz-y^{2}-\left(6y-y^{2}\right)=4$$

To find the opposite of 6y-y^{2}, find the opposite of each term.

$$2z+2y-yz-y^{2}-6y+y^{2}=4$$

Combine 2y and -6y to get -4y.

$$2z-4y-yz-y^{2}+y^{2}=4$$

Combine -y^{2} and y^{2} to get 0.

$$2z-4y-yz=4$$

Add 4y to both sides.

$$2z-yz=4+4y$$

Combine all terms containing z.

$$\left(2-y\right)z=4+4y$$

The equation is in standard form.

$$\left(2-y\right)z=4y+4$$

Divide both sides by 2-y.

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

Dividing by 2-y undoes the multiplication by 2-y.

$$z=\frac{4y+4}{2-y}$$

Divide 4+4y by 2-y.

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