-n^2-5n=6

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

Simplifying
-1n2 + -5n = 6

Reorder the terms:
-5n + -1n2 = 6

Solving
-5n + -1n2 = 6

Solving for variable 'n'.

Reorder the terms:
-6 + -5n + -1n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -5n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5n + n2) = 0

Factor a trinomial.
-1((3 + n)(2 + n)) = 0

Ignore the factor -1.
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 '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Solution
n = {-3, -2}