n^2+6n+6=6

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

Simplifying
n2 + 6n + 6 = 6

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

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

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

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

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

Solving
6n + n2 = 0

Solving for variable 'n'.

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

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

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

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

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