-u^2+2u-1+2u^2+5u+11=0

Solution for -u^2+2u-1+2u^2+5u+11=0 equation:

Simplifying
-1u2 + 2u + -1 + 2u2 + 5u + 11 = 0

Reorder the terms:
-1 + 11 + 2u + 5u + -1u2 + 2u2 = 0

Combine like terms: -1 + 11 = 10
10 + 2u + 5u + -1u2 + 2u2 = 0

Combine like terms: 2u + 5u = 7u
10 + 7u + -1u2 + 2u2 = 0

Combine like terms: -1u2 + 2u2 = 1u2
10 + 7u + 1u2 = 0

Solving
10 + 7u + 1u2 = 0

Solving for variable 'u'.

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

Simplifying
2 + u = 0

Solving
2 + u = 0

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

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

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

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

Simplifying
u = -2
Solution
u = {-5, -2}