7n^2+38n=-15

Solution for 7n^2+38n=-15 equation:

Simplifying
7n2 + 38n = -15

Reorder the terms:
38n + 7n2 = -15

Solving
38n + 7n2 = -15

Solving for variable 'n'.

Reorder the terms:
15 + 38n + 7n2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + 38n + 7n2 = 0

Factor a trinomial.
(5 + n)(3 + 7n) = 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 + 7n)' equal to zero and attempt to solve:

Simplifying
3 + 7n = 0

Solving
3 + 7n = 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 + 7n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7n = 0 + -3
7n = 0 + -3

Combine like terms: 0 + -3 = -3
7n = -3

Divide each side by '7'.
n = -0.4285714286

Simplifying
n = -0.4285714286
Solution
n = {-5, -0.4285714286}