2n(5n+31)=-60

Solution for 2n(5n+31)=-60 equation:

Simplifying
2n(5n + 31) = -60

Reorder the terms:
2n(31 + 5n) = -60
(31 * 2n + 5n * 2n) = -60
(62n + 10n2) = -60

Solving
62n + 10n2 = -60

Solving for variable 'n'.

Reorder the terms:
60 + 62n + 10n2 = -60 + 60

Combine like terms: -60 + 60 = 0
60 + 62n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + 31n + 5n2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

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

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

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

Simplifying
n = -5
Subproblem 2
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
Solution
n = {-5, -1.2}