(2n+2)(6n+1)=0

Solution for (2n+2)(6n+1)=0 equation:

Simplifying
(2n + 2)(6n + 1) = 0

Reorder the terms:
(2 + 2n)(6n + 1) = 0

Reorder the terms:
(2 + 2n)(1 + 6n) = 0

Multiply (2 + 2n) * (1 + 6n)
(2(1 + 6n) + 2n * (1 + 6n)) = 0
((1 * 2 + 6n * 2) + 2n * (1 + 6n)) = 0
((2 + 12n) + 2n * (1 + 6n)) = 0
(2 + 12n + (1 * 2n + 6n * 2n)) = 0
(2 + 12n + (2n + 12n2)) = 0

Combine like terms: 12n + 2n = 14n
(2 + 14n + 12n2) = 0

Solving
2 + 14n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 7n + 6n2) = 0

Factor a trinomial.
2((1 + n)(1 + 6n)) = 0

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

Simplifying
1 + n = 0

Solving
1 + n = 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 + n = 0 + -1

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

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

Simplifying
n = -1
Subproblem 2
Set the factor '(1 + 6n)' equal to zero and attempt to solve:

Simplifying
1 + 6n = 0

Solving
1 + 6n = 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 + 6n = 0 + -1

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

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

Divide each side by '6'.
n = -0.1666666667

Simplifying
n = -0.1666666667
Solution
n = {-1, -0.1666666667}