(5n+2)(6n+5)=0

Solution for (5n+2)(6n+5)=0 equation:

Simplifying
(5n + 2)(6n + 5) = 0

Reorder the terms:
(2 + 5n)(6n + 5) = 0

Reorder the terms:
(2 + 5n)(5 + 6n) = 0

Multiply (2 + 5n) * (5 + 6n)
(2(5 + 6n) + 5n * (5 + 6n)) = 0
((5 * 2 + 6n * 2) + 5n * (5 + 6n)) = 0
((10 + 12n) + 5n * (5 + 6n)) = 0
(10 + 12n + (5 * 5n + 6n * 5n)) = 0
(10 + 12n + (25n + 30n2)) = 0

Combine like terms: 12n + 25n = 37n
(10 + 37n + 30n2) = 0

Solving
10 + 37n + 30n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + 6n)(2 + 5n) = 0

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

Simplifying
5 + 6n = 0

Solving
5 + 6n = 0

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

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

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

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

Divide each side by '6'.
n = -0.8333333333

Simplifying
n = -0.8333333333
Subproblem 2
Set the factor '(2 + 5n)' equal to zero and attempt to solve:

Simplifying
2 + 5n = 0

Solving
2 + 5n = 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 + 5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5n = 0 + -2
5n = 0 + -2

Combine like terms: 0 + -2 = -2
5n = -2

Divide each side by '5'.
n = -0.4

Simplifying
n = -0.4
Solution
n = {-0.8333333333, -0.4}