2n^2+4n+1=10n+1

Solution for 2n^2+4n+1=10n+1 equation:

Simplifying
2n2 + 4n + 1 = 10n + 1

Reorder the terms:
1 + 4n + 2n2 = 10n + 1

Reorder the terms:
1 + 4n + 2n2 = 1 + 10n

Add '-1' to each side of the equation.
1 + 4n + -1 + 2n2 = 1 + -1 + 10n

Reorder the terms:
1 + -1 + 4n + 2n2 = 1 + -1 + 10n

Combine like terms: 1 + -1 = 0
0 + 4n + 2n2 = 1 + -1 + 10n
4n + 2n2 = 1 + -1 + 10n

Combine like terms: 1 + -1 = 0
4n + 2n2 = 0 + 10n
4n + 2n2 = 10n

Solving
4n + 2n2 = 10n

Solving for variable 'n'.

Reorder the terms:
4n + -10n + 2n2 = 10n + -10n

Combine like terms: 4n + -10n = -6n
-6n + 2n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-6n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(-3 + n) = 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 '(-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}