(2n+3)(6n+1)=0

Solution for (2n+3)(6n+1)=0 equation:

Simplifying
(2n + 3)(6n + 1) = 0

Reorder the terms:
(3 + 2n)(6n + 1) = 0

Reorder the terms:
(3 + 2n)(1 + 6n) = 0

Multiply (3 + 2n) * (1 + 6n)
(3(1 + 6n) + 2n * (1 + 6n)) = 0
((1 * 3 + 6n * 3) + 2n * (1 + 6n)) = 0
((3 + 18n) + 2n * (1 + 6n)) = 0
(3 + 18n + (1 * 2n + 6n * 2n)) = 0
(3 + 18n + (2n + 12n2)) = 0

Combine like terms: 18n + 2n = 20n
(3 + 20n + 12n2) = 0

Solving
3 + 20n + 12n2 = 0

Solving for variable 'n'.

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

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

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
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 = {-1.5, -0.1666666667}