5n^2=-11n-6

Solution for 5n^2=-11n-6 equation:

Simplifying
5n2 = -11n + -6

Reorder the terms:
5n2 = -6 + -11n

Solving
5n2 = -6 + -11n

Solving for variable 'n'.

Reorder the terms:
6 + 11n + 5n2 = -6 + -11n + 6 + 11n

Reorder the terms:
6 + 11n + 5n2 = -6 + 6 + -11n + 11n

Combine like terms: -6 + 6 = 0
6 + 11n + 5n2 = 0 + -11n + 11n
6 + 11n + 5n2 = -11n + 11n

Combine like terms: -11n + 11n = 0
6 + 11n + 5n2 = 0

Factor a trinomial.
(6 + 5n)(1 + n) = 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 '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

Add '-1' to each side of the equation.
1 + -1 + n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n = 0 + -1
n = 0 + -1

Combine like terms: 0 + -1 = -1
n = -1

Simplifying
n = -1
Solution
n = {-1.2, -1}