3n^2+23n+42=-2

Solution for 3n^2+23n+42=-2 equation:

Simplifying
3n2 + 23n + 42 = -2

Reorder the terms:
42 + 23n + 3n2 = -2

Solving
42 + 23n + 3n2 = -2

Solving for variable 'n'.

Reorder the terms:
42 + 2 + 23n + 3n2 = -2 + 2

Combine like terms: 42 + 2 = 44
44 + 23n + 3n2 = -2 + 2

Combine like terms: -2 + 2 = 0
44 + 23n + 3n2 = 0

Factor a trinomial.
(4 + n)(11 + 3n) = 0

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 '(11 + 3n)' equal to zero and attempt to solve:

Simplifying
11 + 3n = 0

Solving
11 + 3n = 0

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

Add '-11' to each side of the equation.
11 + -11 + 3n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 3n = 0 + -11
3n = 0 + -11

Combine like terms: 0 + -11 = -11
3n = -11

Divide each side by '3'.
n = -3.666666667

Simplifying
n = -3.666666667
Solution
n = {-4, -3.666666667}