30n^2+61n+30=0

Solution for 30n^2+61n+30=0 equation:

Simplifying
30n2 + 61n + 30 = 0

Reorder the terms:
30 + 61n + 30n2 = 0

Solving
30 + 61n + 30n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(6 + 5n)(5 + 6n) = 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 '(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
Solution
n = {-1.2, -0.8333333333}