n^2-n-342=0

Solution for n^2-n-342=0 equation:

Simplifying
n2 + -1n + -342 = 0

Reorder the terms:
-342 + -1n + n2 = 0

Solving
-342 + -1n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-18 + -1n)(19 + -1n) = 0

Subproblem 1
Set the factor '(-18 + -1n)' equal to zero and attempt to solve:

Simplifying
-18 + -1n = 0

Solving
-18 + -1n = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1n = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1n = 0 + 18
-1n = 0 + 18

Combine like terms: 0 + 18 = 18
-1n = 18

Divide each side by '-1'.
n = -18

Simplifying
n = -18
Subproblem 2
Set the factor '(19 + -1n)' equal to zero and attempt to solve:

Simplifying
19 + -1n = 0

Solving
19 + -1n = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1n = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1n = 0 + -19
-1n = 0 + -19

Combine like terms: 0 + -19 = -19
-1n = -19

Divide each side by '-1'.
n = 19

Simplifying
n = 19
Solution
n = {-18, 19}