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

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

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

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

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

Solving for variable 'n'.

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

Combine like terms: -2n + 11n = 9n
5 + 9n + 4n2 = -11n + 11n

Combine like terms: -11n + 11n = 0
5 + 9n + 4n2 = 0

Factor a trinomial.
(5 + 4n)(1 + n) = 0

Subproblem 1
Set the factor '(5 + 4n)' equal to zero and attempt to solve:

Simplifying
5 + 4n = 0

Solving
5 + 4n = 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 + 4n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4n = 0 + -5
4n = 0 + -5

Combine like terms: 0 + -5 = -5
4n = -5

Divide each side by '4'.
n = -1.25

Simplifying
n = -1.25
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

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

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

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

Simplifying
n = -1
Solution
n = {-1.25, -1}