(15n+7)(3n+6)=0

Solution for (15n+7)(3n+6)=0 equation:

Simplifying
(15n + 7)(3n + 6) = 0

Reorder the terms:
(7 + 15n)(3n + 6) = 0

Reorder the terms:
(7 + 15n)(6 + 3n) = 0

Multiply (7 + 15n) * (6 + 3n)
(7(6 + 3n) + 15n * (6 + 3n)) = 0
((6 * 7 + 3n * 7) + 15n * (6 + 3n)) = 0
((42 + 21n) + 15n * (6 + 3n)) = 0
(42 + 21n + (6 * 15n + 3n * 15n)) = 0
(42 + 21n + (90n + 45n2)) = 0

Combine like terms: 21n + 90n = 111n
(42 + 111n + 45n2) = 0

Solving
42 + 111n + 45n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + 37n + 15n2) = 0

Factor a trinomial.
3((2 + n)(7 + 15n)) = 0

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

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

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

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

Simplifying
n = -2
Subproblem 2
Set the factor '(7 + 15n)' equal to zero and attempt to solve:

Simplifying
7 + 15n = 0

Solving
7 + 15n = 0

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

Add '-7' to each side of the equation.
7 + -7 + 15n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 15n = 0 + -7
15n = 0 + -7

Combine like terms: 0 + -7 = -7
15n = -7

Divide each side by '15'.
n = -0.4666666667

Simplifying
n = -0.4666666667
Solution
n = {-2, -0.4666666667}