6n+2=n^2+2

Solution for 6n+2=n^2+2 equation:

Simplifying
6n + 2 = n2 + 2

Reorder the terms:
2 + 6n = n2 + 2

Reorder the terms:
2 + 6n = 2 + n2

Add '-2' to each side of the equation.
2 + -2 + 6n = 2 + -2 + n2

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

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

Solving
6n = n2

Solving for variable 'n'.

Combine like terms: n2 + -1n2 = 0
6n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(6 + -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 '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {0, 6}