(2u^2)+5=-7u

Solution for (2u^2)+5=-7u equation:

Simplifying
(2u2) + 5 = -7u

Reorder the terms:
5 + (2u2) = -7u

Solving
5 + (2u2) = -7u

Solving for variable 'u'.

Reorder the terms:
5 + 7u + (2u2) = -7u + 7u

Combine like terms: -7u + 7u = 0
5 + 7u + (2u2) = 0

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

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

Simplifying
5 + 2u = 0

Solving
5 + 2u = 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 + 2u = 0 + -5

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

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

Divide each side by '2'.
u = -2.5

Simplifying
u = -2.5
Subproblem 2
Set the factor '(1 + u)' equal to zero and attempt to solve:

Simplifying
1 + u = 0

Solving
1 + u = 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 + u = 0 + -1

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

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

Simplifying
u = -1
Solution
u = {-2.5, -1}