(5n+6)(5n+3)=0

Solution for (5n+6)(5n+3)=0 equation:

Simplifying
(5n + 6)(5n + 3) = 0

Reorder the terms:
(6 + 5n)(5n + 3) = 0

Reorder the terms:
(6 + 5n)(3 + 5n) = 0

Multiply (6 + 5n) * (3 + 5n)
(6(3 + 5n) + 5n * (3 + 5n)) = 0
((3 * 6 + 5n * 6) + 5n * (3 + 5n)) = 0
((18 + 30n) + 5n * (3 + 5n)) = 0
(18 + 30n + (3 * 5n + 5n * 5n)) = 0
(18 + 30n + (15n + 25n2)) = 0

Combine like terms: 30n + 15n = 45n
(18 + 45n + 25n2) = 0

Solving
18 + 45n + 25n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(6 + 5n)(3 + 5n) = 0

Subproblem 1
Set the factor '(6 + 5n)' equal to zero and attempt to solve:

Simplifying
6 + 5n = 0

Solving
6 + 5n = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5n = 0 + -6
5n = 0 + -6

Combine like terms: 0 + -6 = -6
5n = -6

Divide each side by '5'.
n = -1.2

Simplifying
n = -1.2
Subproblem 2
Set the factor '(3 + 5n)' equal to zero and attempt to solve:

Simplifying
3 + 5n = 0

Solving
3 + 5n = 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 + 5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5n = 0 + -3
5n = 0 + -3

Combine like terms: 0 + -3 = -3
5n = -3

Divide each side by '5'.
n = -0.6

Simplifying
n = -0.6
Solution
n = {-1.2, -0.6}