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

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

Simplifying
9n = 2 + 4n + -3n2

Solving
9n = 2 + 4n + -3n2

Solving for variable 'n'.

Reorder the terms:
-2 + 9n + -4n + 3n2 = 2 + 4n + -3n2 + -2 + -4n + 3n2

Combine like terms: 9n + -4n = 5n
-2 + 5n + 3n2 = 2 + 4n + -3n2 + -2 + -4n + 3n2

Reorder the terms:
-2 + 5n + 3n2 = 2 + -2 + 4n + -4n + -3n2 + 3n2

Combine like terms: 2 + -2 = 0
-2 + 5n + 3n2 = 0 + 4n + -4n + -3n2 + 3n2
-2 + 5n + 3n2 = 4n + -4n + -3n2 + 3n2

Combine like terms: 4n + -4n = 0
-2 + 5n + 3n2 = 0 + -3n2 + 3n2
-2 + 5n + 3n2 = -3n2 + 3n2

Combine like terms: -3n2 + 3n2 = 0
-2 + 5n + 3n2 = 0

Factor a trinomial.
(-2 + -1n)(1 + -3n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

Solving
1 + -3n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3n = 0 + -1
-3n = 0 + -1

Combine like terms: 0 + -1 = -1
-3n = -1

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-2, 0.3333333333}