Z+1+(z-2)=(z+3)-1(z+2)

Solution for Z+1+(z-2)=(z+3)-1(z+2) equation:

Simplifying
Z + 1 + (z + -2) = (z + 3) + -1(z + 2)

Reorder the terms:
Z + 1 + (-2 + z) = (z + 3) + -1(z + 2)

Remove parenthesis around (-2 + z)
Z + 1 + -2 + z = (z + 3) + -1(z + 2)

Reorder the terms:
1 + -2 + Z + z = (z + 3) + -1(z + 2)

Combine like terms: 1 + -2 = -1
-1 + Z + z = (z + 3) + -1(z + 2)

Reorder the terms:
-1 + Z + z = (3 + z) + -1(z + 2)

Remove parenthesis around (3 + z)
-1 + Z + z = 3 + z + -1(z + 2)

Reorder the terms:
-1 + Z + z = 3 + z + -1(2 + z)
-1 + Z + z = 3 + z + (2 * -1 + z * -1)
-1 + Z + z = 3 + z + (-2 + -1z)

Reorder the terms:
-1 + Z + z = 3 + -2 + z + -1z

Combine like terms: 3 + -2 = 1
-1 + Z + z = 1 + z + -1z

Combine like terms: z + -1z = 0
-1 + Z + z = 1 + 0
-1 + Z + z = 1

Solving
-1 + Z + z = 1

Solving for variable 'Z'.

Move all terms containing Z to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + Z + 1 + z = 1 + 1

Reorder the terms:
-1 + 1 + Z + z = 1 + 1

Combine like terms: -1 + 1 = 0
0 + Z + z = 1 + 1
Z + z = 1 + 1

Combine like terms: 1 + 1 = 2
Z + z = 2

Add '-1z' to each side of the equation.
Z + z + -1z = 2 + -1z

Combine like terms: z + -1z = 0
Z + 0 = 2 + -1z
Z = 2 + -1z

Simplifying
Z = 2 + -1z