Solve (z+1)(z-2)=(z-4)(z+2)

$$( z + 1 ) ( z - 2 ) = ( z - 4 ) ( z + 2 )$$

Solve for z

$$z=-6$$

Steps for Solving Linear Equation

Use the distributive property to multiply z+1 by z-2 and combine like terms.

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

Use the distributive property to multiply z-4 by z+2 and combine like terms.

$$z^{2}-z-2=z^{2}-2z-8$$

Subtract z^{2} from both sides.

$$z^{2}-z-2-z^{2}=-2z-8$$

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

$$-z-2=-2z-8$$

Add 2z to both sides.

$$-z-2+2z=-8$$

Combine -z and 2z to get z.

$$z-2=-8$$

Add 2 to both sides.

$$z=-8+2$$

Add -8 and 2 to get -6.

$$z=-6$$