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 = 40
40 + 23n + 3n2 = 2 + -2

Combine like terms: 2 + -2 = 0
40 + 23n + 3n2 = 0

Factor a trinomial.
(5 + n)(8 + 3n) = 0

Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(8 + 3n)' equal to zero and attempt to solve:

Simplifying
8 + 3n = 0

Solving
8 + 3n = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3n = 0 + -8
3n = 0 + -8

Combine like terms: 0 + -8 = -8
3n = -8

Divide each side by '3'.
n = -2.666666667

Simplifying
n = -2.666666667
Solution
n = {-5, -2.666666667}