-4n^2+5n-11=2n-6-5n^2

Solution for -4n^2+5n-11=2n-6-5n^2 equation:

Simplifying
-4n2 + 5n + -11 = 2n + -6 + -5n2

Reorder the terms:
-11 + 5n + -4n2 = 2n + -6 + -5n2

Reorder the terms:
-11 + 5n + -4n2 = -6 + 2n + -5n2

Solving
-11 + 5n + -4n2 = -6 + 2n + -5n2

Solving for variable 'n'.

Reorder the terms:
-11 + 6 + 5n + -2n + -4n2 + 5n2 = -6 + 2n + -5n2 + 6 + -2n + 5n2

Combine like terms: -11 + 6 = -5
-5 + 5n + -2n + -4n2 + 5n2 = -6 + 2n + -5n2 + 6 + -2n + 5n2

Combine like terms: 5n + -2n = 3n
-5 + 3n + -4n2 + 5n2 = -6 + 2n + -5n2 + 6 + -2n + 5n2

Combine like terms: -4n2 + 5n2 = 1n2
-5 + 3n + 1n2 = -6 + 2n + -5n2 + 6 + -2n + 5n2

Reorder the terms:
-5 + 3n + 1n2 = -6 + 6 + 2n + -2n + -5n2 + 5n2

Combine like terms: -6 + 6 = 0
-5 + 3n + 1n2 = 0 + 2n + -2n + -5n2 + 5n2
-5 + 3n + 1n2 = 2n + -2n + -5n2 + 5n2

Combine like terms: 2n + -2n = 0
-5 + 3n + 1n2 = 0 + -5n2 + 5n2
-5 + 3n + 1n2 = -5n2 + 5n2

Combine like terms: -5n2 + 5n2 = 0
-5 + 3n + 1n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3n + 5 + n2 = 0 + 5

Reorder the terms:
-5 + 5 + 3n + n2 = 0 + 5

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

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

The n term is 3n.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3n + 2.25 + n2 = 5 + 2.25

Reorder the terms:
2.25 + 3n + n2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + 3n + n2 = 7.25

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(n + 1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
n + 1.5 = 2.692582404

Simplifying
n + 1.5 = 2.692582404

Reorder the terms:
1.5 + n = 2.692582404

Solving
1.5 + n = 2.692582404

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = 2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = 2.692582404 + -1.5
n = 2.692582404 + -1.5

Combine like terms: 2.692582404 + -1.5 = 1.192582404
n = 1.192582404

Simplifying
n = 1.192582404

Subproblem 2
n + 1.5 = -2.692582404

Simplifying
n + 1.5 = -2.692582404

Reorder the terms:
1.5 + n = -2.692582404

Solving
1.5 + n = -2.692582404

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = -2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = -2.692582404 + -1.5
n = -2.692582404 + -1.5

Combine like terms: -2.692582404 + -1.5 = -4.192582404
n = -4.192582404

Simplifying
n = -4.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.192582404, -4.192582404}