n^2+n=380

Solution for n^2+n=380 equation:

Simplifying
n2 + n = 380

Reorder the terms:
n + n2 = 380

Solving
n + n2 = 380

Solving for variable 'n'.

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

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

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

Subproblem 1
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
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 = {-20, 19}