-2n^2-9n+11=-4n^2+1

Solution for -2n^2-9n+11=-4n^2+1 equation:

Simplifying
-2n2 + -9n + 11 = -4n2 + 1

Reorder the terms:
11 + -9n + -2n2 = -4n2 + 1

Reorder the terms:
11 + -9n + -2n2 = 1 + -4n2

Solving
11 + -9n + -2n2 = 1 + -4n2

Solving for variable 'n'.

Reorder the terms:
11 + -1 + -9n + -2n2 + 4n2 = 1 + -4n2 + -1 + 4n2

Combine like terms: 11 + -1 = 10
10 + -9n + -2n2 + 4n2 = 1 + -4n2 + -1 + 4n2

Combine like terms: -2n2 + 4n2 = 2n2
10 + -9n + 2n2 = 1 + -4n2 + -1 + 4n2

Reorder the terms:
10 + -9n + 2n2 = 1 + -1 + -4n2 + 4n2

Combine like terms: 1 + -1 = 0
10 + -9n + 2n2 = 0 + -4n2 + 4n2
10 + -9n + 2n2 = -4n2 + 4n2

Combine like terms: -4n2 + 4n2 = 0
10 + -9n + 2n2 = 0

Factor a trinomial.
(2 + -1n)(5 + -2n) = 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 '(5 + -2n)' equal to zero and attempt to solve:

Simplifying
5 + -2n = 0

Solving
5 + -2n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2n = 0 + -5

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

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

Divide each side by '-2'.
n = 2.5

Simplifying
n = 2.5
Solution
n = {2, 2.5}