2n^2+4n+1=10n+9

Solution for 2n^2+4n+1=10n+9 equation:

Simplifying
2n2 + 4n + 1 = 10n + 9

Reorder the terms:
1 + 4n + 2n2 = 10n + 9

Reorder the terms:
1 + 4n + 2n2 = 9 + 10n

Solving
1 + 4n + 2n2 = 9 + 10n

Solving for variable 'n'.

Reorder the terms:
1 + -9 + 4n + -10n + 2n2 = 9 + 10n + -9 + -10n

Combine like terms: 1 + -9 = -8
-8 + 4n + -10n + 2n2 = 9 + 10n + -9 + -10n

Combine like terms: 4n + -10n = -6n
-8 + -6n + 2n2 = 9 + 10n + -9 + -10n

Reorder the terms:
-8 + -6n + 2n2 = 9 + -9 + 10n + -10n

Combine like terms: 9 + -9 = 0
-8 + -6n + 2n2 = 0 + 10n + -10n
-8 + -6n + 2n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-8 + -6n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -3n + n2) = 0

Factor a trinomial.
2((-1 + -1n)(4 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

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

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

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-1, 4}