-3n(n+5)=12

Solution for -3n(n+5)=12 equation:

Simplifying
-3n(n + 5) = 12

Reorder the terms:
-3n(5 + n) = 12
(5 * -3n + n * -3n) = 12
(-15n + -3n2) = 12

Solving
-15n + -3n2 = 12

Solving for variable 'n'.

Reorder the terms:
-12 + -15n + -3n2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -15n + -3n2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(4 + 5n + n2) = 0

Factor a trinomial.
-3((4 + n)(1 + n)) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

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

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

Simplifying
n = -4
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 = {-4, -1}