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

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

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

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

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

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

Combine like terms: 6n + 12n = 18n
(6 + 18n + 12n2) = 0

Solving
6 + 18n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 3n + 2n2) = 0

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

Ignore the factor 6.
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 + 2n)' equal to zero and attempt to solve:

Simplifying
1 + 2n = 0

Solving
1 + 2n = 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 + 2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2n = 0 + -1
2n = 0 + -1

Combine like terms: 0 + -1 = -1
2n = -1

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
Solution
n = {-1, -0.5}