2n^2=11n-5

Solution for 2n^2=11n-5 equation:

Simplifying
2n2 = 11n + -5

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

Solving
2n2 = -5 + 11n

Solving for variable 'n'.

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

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

Combine like terms: -5 + 5 = 0
5 + -11n + 2n2 = 0 + 11n + -11n
5 + -11n + 2n2 = 11n + -11n

Combine like terms: 11n + -11n = 0
5 + -11n + 2n2 = 0

Factor a trinomial.
(1 + -2n)(5 + -1n) = 0

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

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

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

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

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {0.5, 5}