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

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

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

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

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

Multiply (6 + 2n) * (1 + 6n)
(6(1 + 6n) + 2n * (1 + 6n)) = 0
((1 * 6 + 6n * 6) + 2n * (1 + 6n)) = 0
((6 + 36n) + 2n * (1 + 6n)) = 0
(6 + 36n + (1 * 2n + 6n * 2n)) = 0
(6 + 36n + (2n + 12n2)) = 0

Combine like terms: 36n + 2n = 38n
(6 + 38n + 12n2) = 0

Solving
6 + 38n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 19n + 6n2) = 0

Factor a trinomial.
2((3 + n)(1 + 6n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
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 = {-3, -0.1666666667}