Z^2=-2Z+3

Solution for Z^2=-2Z+3 equation:

Simplifying
Z2 = -2Z + 3

Reorder the terms:
Z2 = 3 + -2Z

Solving
Z2 = 3 + -2Z

Solving for variable 'Z'.

Reorder the terms:
-3 + 2Z + Z2 = 3 + -2Z + -3 + 2Z

Reorder the terms:
-3 + 2Z + Z2 = 3 + -3 + -2Z + 2Z

Combine like terms: 3 + -3 = 0
-3 + 2Z + Z2 = 0 + -2Z + 2Z
-3 + 2Z + Z2 = -2Z + 2Z

Combine like terms: -2Z + 2Z = 0
-3 + 2Z + Z2 = 0

Factor a trinomial.
(-3 + -1Z)(1 + -1Z) = 0

Subproblem 1
Set the factor '(-3 + -1Z)' equal to zero and attempt to solve:

Simplifying
-3 + -1Z = 0

Solving
-3 + -1Z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1Z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1Z = 0 + 3
-1Z = 0 + 3

Combine like terms: 0 + 3 = 3
-1Z = 3

Divide each side by '-1'.
Z = -3

Simplifying
Z = -3
Subproblem 2
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
Solution
Z = {-3, 1}