15n(n+3)=11n-15

Solution for 15n(n+3)=11n-15 equation:

Simplifying
15n(n + 3) = 11n + -15

Reorder the terms:
15n(3 + n) = 11n + -15
(3 * 15n + n * 15n) = 11n + -15
(45n + 15n2) = 11n + -15

Reorder the terms:
45n + 15n2 = -15 + 11n

Solving
45n + 15n2 = -15 + 11n

Solving for variable 'n'.

Reorder the terms:
15 + 45n + -11n + 15n2 = -15 + 11n + 15 + -11n

Combine like terms: 45n + -11n = 34n
15 + 34n + 15n2 = -15 + 11n + 15 + -11n

Reorder the terms:
15 + 34n + 15n2 = -15 + 15 + 11n + -11n

Combine like terms: -15 + 15 = 0
15 + 34n + 15n2 = 0 + 11n + -11n
15 + 34n + 15n2 = 11n + -11n

Combine like terms: 11n + -11n = 0
15 + 34n + 15n2 = 0

Factor a trinomial.
(5 + 3n)(3 + 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 '(3 + 5n)' equal to zero and attempt to solve:

Simplifying
3 + 5n = 0

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

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

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

Divide each side by '5'.
n = -0.6

Simplifying
n = -0.6
Solution
n = {-1.666666667, -0.6}