6n^2+8n+9n+12=0

Solution for 6n^2+8n+9n+12=0 equation:

Simplifying
6n2 + 8n + 9n + 12 = 0

Reorder the terms:
12 + 8n + 9n + 6n2 = 0

Combine like terms: 8n + 9n = 17n
12 + 17n + 6n2 = 0

Solving
12 + 17n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + 2n)(4 + 3n) = 0

Subproblem 1
Set the factor '(3 + 2n)' equal to zero and attempt to solve:

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(4 + 3n)' equal to zero and attempt to solve:

Simplifying
4 + 3n = 0

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

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

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

Divide each side by '3'.
n = -1.333333333

Simplifying
n = -1.333333333
Solution
n = {-1.5, -1.333333333}