n*(2n-1)=1

Solution for n*(2n-1)=1 equation:

Simplifying
n(2n + -1) = 1

Reorder the terms:
n(-1 + 2n) = 1
(-1 * n + 2n * n) = 1
(-1n + 2n2) = 1

Solving
-1n + 2n2 = 1

Solving for variable 'n'.

Reorder the terms:
-1 + -1n + 2n2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -1n + 2n2 = 0

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

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

Simplifying
-1 + -2n = 0

Solving
-1 + -2n = 0

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

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

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

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

Divide each side by '-2'.
n = -0.5

Simplifying
n = -0.5
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Solution
n = {-0.5, 1}