u^2=2u-1

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

Simplifying
u2 = 2u + -1

Reorder the terms:
u2 = -1 + 2u

Solving
u2 = -1 + 2u

Solving for variable 'u'.

Reorder the terms:
1 + -2u + u2 = -1 + 2u + 1 + -2u

Reorder the terms:
1 + -2u + u2 = -1 + 1 + 2u + -2u

Combine like terms: -1 + 1 = 0
1 + -2u + u2 = 0 + 2u + -2u
1 + -2u + u2 = 2u + -2u

Combine like terms: 2u + -2u = 0
1 + -2u + u2 = 0

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

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

Simplifying
1 + -1u = 0

Solving
1 + -1u = 0

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

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

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

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

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

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

Simplifying
1 + -1u = 0

Solving
1 + -1u = 0

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

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

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

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

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

Simplifying
u = 1
Solution
u = {1, 1}