z^2-2z=2-z

Solution for z^2-2z=2-z equation:

Simplifying
z2 + -2z = 2 + -1z

Reorder the terms:
-2z + z2 = 2 + -1z

Solving
-2z + z2 = 2 + -1z

Solving for variable 'z'.

Reorder the terms:
-2 + -2z + z + z2 = 2 + -1z + -2 + z

Combine like terms: -2z + z = -1z
-2 + -1z + z2 = 2 + -1z + -2 + z

Reorder the terms:
-2 + -1z + z2 = 2 + -2 + -1z + z

Combine like terms: 2 + -2 = 0
-2 + -1z + z2 = 0 + -1z + z
-2 + -1z + z2 = -1z + z

Combine like terms: -1z + z = 0
-2 + -1z + z2 = 0

Factor a trinomial.
(-1 + -1z)(2 + -1z) = 0

Subproblem 1
Set the factor '(-1 + -1z)' equal to zero and attempt to solve:

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1z = 0 + 1

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

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

Divide each side by '-1'.
z = -1

Simplifying
z = -1
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-1, 2}