0=n^2+9n-400

Solution for 0=n^2+9n-400 equation:

Simplifying
0 = n2 + 9n + -400

Reorder the terms:
0 = -400 + 9n + n2

Solving
0 = -400 + 9n + n2

Solving for variable 'n'.

Combine like terms: 0 + 400 = 400
400 + -9n + -1n2 = -400 + 9n + n2 + 400 + -9n + -1n2

Reorder the terms:
400 + -9n + -1n2 = -400 + 400 + 9n + -9n + n2 + -1n2

Combine like terms: -400 + 400 = 0
400 + -9n + -1n2 = 0 + 9n + -9n + n2 + -1n2
400 + -9n + -1n2 = 9n + -9n + n2 + -1n2

Combine like terms: 9n + -9n = 0
400 + -9n + -1n2 = 0 + n2 + -1n2
400 + -9n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
400 + -9n + -1n2 = 0

Factor a trinomial.
(16 + -1n)(25 + n) = 0

Subproblem 1
Set the factor '(16 + -1n)' equal to zero and attempt to solve:

Simplifying
16 + -1n = 0

Solving
16 + -1n = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1n = 0 + -16
-1n = 0 + -16

Combine like terms: 0 + -16 = -16
-1n = -16

Divide each side by '-1'.
n = 16

Simplifying
n = 16
Subproblem 2
Set the factor '(25 + n)' equal to zero and attempt to solve:

Simplifying
25 + n = 0

Solving
25 + n = 0

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

Add '-25' to each side of the equation.
25 + -25 + n = 0 + -25

Combine like terms: 25 + -25 = 0
0 + n = 0 + -25
n = 0 + -25

Combine like terms: 0 + -25 = -25
n = -25

Simplifying
n = -25
Solution
n = {16, -25}