2u(u+1)+5(u+1)=

Solution for 2u(u+1)+5(u+1)= equation:

Simplifying
2u(u + 1) + 5(u + 1) = 0

Reorder the terms:
2u(1 + u) + 5(u + 1) = 0
(1 * 2u + u * 2u) + 5(u + 1) = 0
(2u + 2u2) + 5(u + 1) = 0

Reorder the terms:
2u + 2u2 + 5(1 + u) = 0
2u + 2u2 + (1 * 5 + u * 5) = 0
2u + 2u2 + (5 + 5u) = 0

Reorder the terms:
5 + 2u + 5u + 2u2 = 0

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

Solving
5 + 7u + 2u2 = 0

Solving for variable 'u'.

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}