n=n(2n-1)

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

Simplifying
n = n(2n + -1)

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

Solving
n = -1n + 2n2

Solving for variable 'n'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2n'.
2n(1 + -1n) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
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, 1}