0=-630+9n+n^2

Solution for 0=-630+9n+n^2 equation:

Simplifying
0 = -630 + 9n + n2

Solving
0 = -630 + 9n + n2

Solving for variable 'n'.

Combine like terms: 0 + 630 = 630
630 + -9n + -1n2 = -630 + 9n + n2 + 630 + -9n + -1n2

Reorder the terms:
630 + -9n + -1n2 = -630 + 630 + 9n + -9n + n2 + -1n2

Combine like terms: -630 + 630 = 0
630 + -9n + -1n2 = 0 + 9n + -9n + n2 + -1n2
630 + -9n + -1n2 = 9n + -9n + n2 + -1n2

Combine like terms: 9n + -9n = 0
630 + -9n + -1n2 = 0 + n2 + -1n2
630 + -9n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
630 + -9n + -1n2 = 0

Factor a trinomial.
(21 + -1n)(30 + n) = 0

Subproblem 1
Set the factor '(21 + -1n)' equal to zero and attempt to solve:

Simplifying
21 + -1n = 0

Solving
21 + -1n = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1n = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1n = 0 + -21
-1n = 0 + -21

Combine like terms: 0 + -21 = -21
-1n = -21

Divide each side by '-1'.
n = 21

Simplifying
n = 21
Subproblem 2
Set the factor '(30 + n)' equal to zero and attempt to solve:

Simplifying
30 + n = 0

Solving
30 + n = 0

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

Add '-30' to each side of the equation.
30 + -30 + n = 0 + -30

Combine like terms: 30 + -30 = 0
0 + n = 0 + -30
n = 0 + -30

Combine like terms: 0 + -30 = -30
n = -30

Simplifying
n = -30
Solution
n = {21, -30}