18n^2+60n+42=0

Solution for 18n^2+60n+42=0 equation:

Simplifying
18n2 + 60n + 42 = 0

Reorder the terms:
42 + 60n + 18n2 = 0

Solving
42 + 60n + 18n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + 10n + 3n2) = 0

Factor a trinomial.
6((7 + 3n)(1 + n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(7 + 3n)' equal to zero and attempt to solve:

Simplifying
7 + 3n = 0

Solving
7 + 3n = 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 + 3n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3n = 0 + -7
3n = 0 + -7

Combine like terms: 0 + -7 = -7
3n = -7

Divide each side by '3'.
n = -2.333333333

Simplifying
n = -2.333333333
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 = {-2.333333333, -1}