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

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

Solve for z

$$z=5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 3z-5.

$$6z-10-3\left(2+z\right)=5-\left(z+1\right)$$

Use the distributive property to multiply -3 by 2+z.

$$6z-10-6-3z=5-\left(z+1\right)$$

Subtract 6 from -10 to get -16.

$$6z-16-3z=5-\left(z+1\right)$$

Combine 6z and -3z to get 3z.

$$3z-16=5-\left(z+1\right)$$

To find the opposite of z+1, find the opposite of each term.

$$3z-16=5-z-1$$

Subtract 1 from 5 to get 4.

$$3z-16=4-z$$

Add z to both sides.

$$3z-16+z=4$$

Combine 3z and z to get 4z.

$$4z-16=4$$

Add 16 to both sides.

$$4z=4+16$$

Add 4 and 16 to get 20.

$$4z=20$$

Divide both sides by 4.

$$z=\frac{20}{4}$$

Divide 20 by 4 to get 5.

$$z=5$$