A^2-2A=-1

Solution for A^2-2A=-1 equation:

Simplifying
A2 + -2A = -1

Reorder the terms:
-2A + A2 = -1

Solving
-2A + A2 = -1

Solving for variable 'A'.

Reorder the terms:
1 + -2A + A2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -2A + A2 = 0

Factor a trinomial.
(1 + -1A)(1 + -1A) = 0

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

Simplifying
1 + -1A = 0

Solving
1 + -1A = 0

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

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

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

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

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

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

Simplifying
1 + -1A = 0

Solving
1 + -1A = 0

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

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

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

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

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

Simplifying
A = 1
Solution
A = {1, 1}