n^2-n=380

Solution for n^2-n=380 equation:

Simplifying
n2 + -1n = 380

Reorder the terms:
-1n + n2 = 380

Solving
-1n + n2 = 380

Solving for variable 'n'.

Reorder the terms:
-380 + -1n + n2 = 380 + -380

Combine like terms: 380 + -380 = 0
-380 + -1n + n2 = 0

Factor a trinomial.
(-19 + -1n)(20 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(20 + -1n)' equal to zero and attempt to solve:

Simplifying
20 + -1n = 0

Solving
20 + -1n = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1n = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1n = 0 + -20
-1n = 0 + -20

Combine like terms: 0 + -20 = -20
-1n = -20

Divide each side by '-1'.
n = 20

Simplifying
n = 20
Solution
n = {-19, 20}