23n^2-19n-42=0

Solution for 23n^2-19n-42=0 equation:

Simplifying
23n2 + -19n + -42 = 0

Reorder the terms:
-42 + -19n + 23n2 = 0

Solving
-42 + -19n + 23n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -1n)(42 + -23n) = 0

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 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 + -1n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1n = 0 + 1
-1n = 0 + 1

Combine like terms: 0 + 1 = 1
-1n = 1

Divide each side by '-1'.
n = -1

Simplifying
n = -1
Subproblem 2
Set the factor '(42 + -23n)' equal to zero and attempt to solve:

Simplifying
42 + -23n = 0

Solving
42 + -23n = 0

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

Add '-42' to each side of the equation.
42 + -42 + -23n = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -23n = 0 + -42
-23n = 0 + -42

Combine like terms: 0 + -42 = -42
-23n = -42

Divide each side by '-23'.
n = 1.826086957

Simplifying
n = 1.826086957
Solution
n = {-1, 1.826086957}