15n^2+57n+36=0

Solution for 15n^2+57n+36=0 equation:

Simplifying
15n2 + 57n + 36 = 0

Reorder the terms:
36 + 57n + 15n2 = 0

Solving
36 + 57n + 15n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 19n + 5n2) = 0

Factor a trinomial.
3((3 + n)(4 + 5n)) = 0

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

Simplifying
3 + n = 0

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

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

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

Simplifying
n = -3
Subproblem 2
Set the factor '(4 + 5n)' equal to zero and attempt to solve:

Simplifying
4 + 5n = 0

Solving
4 + 5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5n = 0 + -4
5n = 0 + -4

Combine like terms: 0 + -4 = -4
5n = -4

Divide each side by '5'.
n = -0.8

Simplifying
n = -0.8
Solution
n = {-3, -0.8}