(4n+1)(2n+6)=0

Solution for (4n+1)(2n+6)=0 equation:

Simplifying
(4n + 1)(2n + 6) = 0

Reorder the terms:
(1 + 4n)(2n + 6) = 0

Reorder the terms:
(1 + 4n)(6 + 2n) = 0

Multiply (1 + 4n) * (6 + 2n)
(1(6 + 2n) + 4n * (6 + 2n)) = 0
((6 * 1 + 2n * 1) + 4n * (6 + 2n)) = 0
((6 + 2n) + 4n * (6 + 2n)) = 0
(6 + 2n + (6 * 4n + 2n * 4n)) = 0
(6 + 2n + (24n + 8n2)) = 0

Combine like terms: 2n + 24n = 26n
(6 + 26n + 8n2) = 0

Solving
6 + 26n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 13n + 4n2) = 0

Factor a trinomial.
2((3 + n)(1 + 4n)) = 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 + 4n)' equal to zero and attempt to solve:

Simplifying
1 + 4n = 0

Solving
1 + 4n = 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 + 4n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4n = 0 + -1
4n = 0 + -1

Combine like terms: 0 + -1 = -1
4n = -1

Divide each side by '4'.
n = -0.25

Simplifying
n = -0.25
Solution
n = {-3, -0.25}