Solve (z+9)(z-2)=(z+6)(z-20)

$$( z + 9 ) ( z - 2 ) = ( z + 6 ) ( z - 20 )$$

Solve for z

$$z = -\frac{34}{7} = -4\frac{6}{7} \approx -4.857142857$$

Steps for Solving Linear Equation

Use the distributive property to multiply z+9 by z-2 and combine like terms.

$$z^{2}+7z-18=\left(z+6\right)\left(z-20\right)$$

Use the distributive property to multiply z+6 by z-20 and combine like terms.

$$z^{2}+7z-18=z^{2}-14z-120$$

Subtract z^{2} from both sides.

$$z^{2}+7z-18-z^{2}=-14z-120$$

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

$$7z-18=-14z-120$$

Add 14z to both sides.

$$7z-18+14z=-120$$

Combine 7z and 14z to get 21z.

$$21z-18=-120$$

Add 18 to both sides.

$$21z=-120+18$$

Add -120 and 18 to get -102.

$$21z=-102$$

Divide both sides by 21.

$$z=\frac{-102}{21}$$

Reduce the fraction \frac{-102}{21} to lowest terms by extracting and canceling out 3.

$$z=-\frac{34}{7}$$