n^2+4n+1=1+n

Solution for n^2+4n+1=1+n equation:

Simplifying
n2 + 4n + 1 = 1 + n

Reorder the terms:
1 + 4n + n2 = 1 + n

Add '-1' to each side of the equation.
1 + 4n + -1 + n2 = 1 + -1 + n

Reorder the terms:
1 + -1 + 4n + n2 = 1 + -1 + n

Combine like terms: 1 + -1 = 0
0 + 4n + n2 = 1 + -1 + n
4n + n2 = 1 + -1 + n

Combine like terms: 1 + -1 = 0
4n + n2 = 0 + n
4n + n2 = n

Solving
4n + n2 = n

Solving for variable 'n'.

Reorder the terms:
4n + -1n + n2 = n + -1n

Combine like terms: 4n + -1n = 3n
3n + n2 = n + -1n

Combine like terms: n + -1n = 0
3n + n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(3 + 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 '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Solution
n = {0, -3}