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.
(-25 + -1n)(16 + -1n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-25, 16}