n^2-9n-400=0

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

Simplifying
n2 + -9n + -400 = 0

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

Solving
-400 + -9n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-16 + -1n)(25 + -1n) = 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 + -1n)' equal to zero and attempt to solve:

Simplifying
25 + -1n = 0

Solving
25 + -1n = 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 + -1n = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1n = 0 + -25
-1n = 0 + -25

Combine like terms: 0 + -25 = -25
-1n = -25

Divide each side by '-1'.
n = 25

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