n*n+n+1=2n+1

Solution for n*n+n+1=2n+1 equation:

Simplifying
n * n + n + 1 = 2n + 1

Multiply n * n
n2 + n + 1 = 2n + 1

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

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

Add '-1' to each side of the equation.
1 + n + -1 + n2 = 1 + -1 + 2n

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

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

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

Solving
n + n2 = 2n

Solving for variable 'n'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1 + n) = 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 + n)' equal to zero and attempt to solve:

Simplifying
-1 + n = 0

Solving
-1 + n = 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 + n = 0 + 1

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

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

Simplifying
n = 1
Solution
n = {0, 1}