2n^2+11n=3n-n^2-4

Solution for 2n^2+11n=3n-n^2-4 equation:

Simplifying
2n2 + 11n = 3n + -1n2 + -4

Reorder the terms:
11n + 2n2 = 3n + -1n2 + -4

Reorder the terms:
11n + 2n2 = -4 + 3n + -1n2

Solving
11n + 2n2 = -4 + 3n + -1n2

Solving for variable 'n'.

Reorder the terms:
4 + 11n + -3n + 2n2 + n2 = -4 + 3n + -1n2 + 4 + -3n + n2

Combine like terms: 11n + -3n = 8n
4 + 8n + 2n2 + n2 = -4 + 3n + -1n2 + 4 + -3n + n2

Combine like terms: 2n2 + n2 = 3n2
4 + 8n + 3n2 = -4 + 3n + -1n2 + 4 + -3n + n2

Reorder the terms:
4 + 8n + 3n2 = -4 + 4 + 3n + -3n + -1n2 + n2

Combine like terms: -4 + 4 = 0
4 + 8n + 3n2 = 0 + 3n + -3n + -1n2 + n2
4 + 8n + 3n2 = 3n + -3n + -1n2 + n2

Combine like terms: 3n + -3n = 0
4 + 8n + 3n2 = 0 + -1n2 + n2
4 + 8n + 3n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
4 + 8n + 3n2 = 0

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

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

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

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

Simplifying
2 + 3n = 0

Solving
2 + 3n = 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 + 3n = 0 + -2

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

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

Divide each side by '3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
Solution
n = {-2, -0.6666666667}