4n^2+23n+15=0

Solution for 4n^2+23n+15=0 equation:

Simplifying
4n2 + 23n + 15 = 0

Reorder the terms:
15 + 23n + 4n2 = 0

Solving
15 + 23n + 4n2 = 0

Solving for variable 'n'.

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

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 '(3 + 4n)' equal to zero and attempt to solve:

Simplifying
3 + 4n = 0

Solving
3 + 4n = 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 + 4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4n = 0 + -3
4n = 0 + -3

Combine like terms: 0 + -3 = -3
4n = -3

Divide each side by '4'.
n = -0.75

Simplifying
n = -0.75
Solution
n = {-5, -0.75}