Solve (2z+5)(z-3)=(z-6)(2z-2)-1

$$( 2 z + 5 ) ( z - 3 ) = ( z - 6 ) ( 2 z - 2 ) - 1$$

Solve for z

$$z=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2z+5 by z-3 and combine like terms.

$$2z^{2}-z-15=\left(z-6\right)\left(2z-2\right)-1$$

Use the distributive property to multiply z-6 by 2z-2 and combine like terms.

$$2z^{2}-z-15=2z^{2}-14z+12-1$$

Subtract 1 from 12 to get 11.

$$2z^{2}-z-15=2z^{2}-14z+11$$

Subtract 2z^{2} from both sides.

$$2z^{2}-z-15-2z^{2}=-14z+11$$

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

$$-z-15=-14z+11$$

Add 14z to both sides.

$$-z-15+14z=11$$

Combine -z and 14z to get 13z.

$$13z-15=11$$

Add 15 to both sides.

$$13z=11+15$$

Add 11 and 15 to get 26.

$$13z=26$$

Divide both sides by 13.

$$z=\frac{26}{13}$$

Divide 26 by 13 to get 2.

$$z=2$$