2n^2+n=9-2n

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

Simplifying
2n2 + n = 9 + -2n

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

Solving
n + 2n2 = 9 + -2n

Solving for variable 'n'.

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

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

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

Combine like terms: 9 + -9 = 0
-9 + 3n + 2n2 = 0 + -2n + 2n
-9 + 3n + 2n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
-9 + 3n + 2n2 = 0

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

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

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

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

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

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

Divide each side by '-1'.
n = -3

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

Simplifying
3 + -2n = 0

Solving
3 + -2n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2n = 0 + -3

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

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

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {-3, 1.5}