2n=n^2+n

Solution for 2n=n^2+n equation:

Simplifying
2n = n2 + n

Reorder the terms:
2n = n + n2

Solving
2n = n + n2

Solving for variable 'n'.

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

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

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

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

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

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}