2U^2=-11U-5

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

Simplifying
2U2 = -11U + -5

Reorder the terms:
2U2 = -5 + -11U

Solving
2U2 = -5 + -11U

Solving for variable 'U'.

Reorder the terms:
5 + 11U + 2U2 = -5 + -11U + 5 + 11U

Reorder the terms:
5 + 11U + 2U2 = -5 + 5 + -11U + 11U

Combine like terms: -5 + 5 = 0
5 + 11U + 2U2 = 0 + -11U + 11U
5 + 11U + 2U2 = -11U + 11U

Combine like terms: -11U + 11U = 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}