z^2-2z=-2+z

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

Simplifying
z2 + -2z = -2 + z

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

Solving
-2z + z2 = -2 + z

Solving for variable 'z'.

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

Combine like terms: -2z + -1z = -3z
2 + -3z + z2 = -2 + z + 2 + -1z

Reorder the terms:
2 + -3z + z2 = -2 + 2 + z + -1z

Combine like terms: -2 + 2 = 0
2 + -3z + z2 = 0 + z + -1z
2 + -3z + z2 = z + -1z

Combine like terms: z + -1z = 0
2 + -3z + 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}