12n^2+54n+42=0

Solution for 12n^2+54n+42=0 equation:

Simplifying
12n2 + 54n + 42 = 0

Reorder the terms:
42 + 54n + 12n2 = 0

Solving
42 + 54n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + 9n + 2n2) = 0

Factor a trinomial.
6((7 + 2n)(1 + n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(7 + 2n)' equal to zero and attempt to solve:

Simplifying
7 + 2n = 0

Solving
7 + 2n = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2n = 0 + -7
2n = 0 + -7

Combine like terms: 0 + -7 = -7
2n = -7

Divide each side by '2'.
n = -3.5

Simplifying
n = -3.5
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 = {-3.5, -1}