Solve (z+6):(z-8)=(z-7):(z+9)

$$( z + 6 ) : ( z - 8 ) = ( z - 7 ) : ( z + 9 )$$

Solve for z

$$z=\frac{1}{15}\approx 0.066666667$$

Steps for Solving Linear Equation

Variable z cannot be equal to any of the values -9,8 since division by zero is not defined. Multiply both sides of the equation by \left(z-8\right)\left(z+9\right), the least common multiple of z-8,z+9.

$$\left(z+9\right)\left(z+6\right)=\left(z-8\right)\left(z-7\right)$$

Use the distributive property to multiply z+9 by z+6 and combine like terms.

$$z^{2}+15z+54=\left(z-8\right)\left(z-7\right)$$

Use the distributive property to multiply z-8 by z-7 and combine like terms.

$$z^{2}+15z+54=z^{2}-15z+56$$

Subtract z^{2} from both sides.

$$z^{2}+15z+54-z^{2}=-15z+56$$

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

$$15z+54=-15z+56$$

Add 15z to both sides.

$$15z+54+15z=56$$

Combine 15z and 15z to get 30z.

$$30z+54=56$$

Subtract 54 from both sides.

$$30z=56-54$$

Subtract 54 from 56 to get 2.

$$30z=2$$

Divide both sides by 30.

$$z=\frac{2}{30}$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$z=\frac{1}{15}$$