-9=-4n+3-n^2

Solution for -9=-4n+3-n^2 equation:

Simplifying
-9 = -4n + 3 + -1n2

Reorder the terms:
-9 = 3 + -4n + -1n2

Solving
-9 = 3 + -4n + -1n2

Solving for variable 'n'.

Combine like terms: -9 + -3 = -12
-12 + 4n + n2 = 3 + -4n + -1n2 + -3 + 4n + n2

Reorder the terms:
-12 + 4n + n2 = 3 + -3 + -4n + 4n + -1n2 + n2

Combine like terms: 3 + -3 = 0
-12 + 4n + n2 = 0 + -4n + 4n + -1n2 + n2
-12 + 4n + n2 = -4n + 4n + -1n2 + n2

Combine like terms: -4n + 4n = 0
-12 + 4n + n2 = 0 + -1n2 + n2
-12 + 4n + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-12 + 4n + n2 = 0

Factor a trinomial.
(-6 + -1n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-6, 2}