15n^2+31n+10=0

Solution for 15n^2+31n+10=0 equation:

Simplifying
15n2 + 31n + 10 = 0

Reorder the terms:
10 + 31n + 15n2 = 0

Solving
10 + 31n + 15n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(5 + 3n)(2 + 5n) = 0

Subproblem 1
Set the factor '(5 + 3n)' equal to zero and attempt to solve:

Simplifying
5 + 3n = 0

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

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

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

Divide each side by '3'.
n = -1.666666667

Simplifying
n = -1.666666667
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 = {-1.666666667, -0.4}