2u^2+11u=-5

Solution for 2u^2+11u=-5 equation:

Simplifying
2u2 + 11u = -5

Reorder the terms:
11u + 2u2 = -5

Solving
11u + 2u2 = -5

Solving for variable 'u'.

Reorder the terms:
5 + 11u + 2u2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 11u + 2u2 = 0

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

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

Simplifying
5 + u = 0

Solving
5 + u = 0

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

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

Combine like terms: 5 + -5 = 0
0 + u = 0 + -5
u = 0 + -5

Combine like terms: 0 + -5 = -5
u = -5

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

Simplifying
1 + 2u = 0

Solving
1 + 2u = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2u = 0 + -1

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

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

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

Simplifying
u = -0.5
Solution
u = {-5, -0.5}