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

Solution for (u+2)(u+5)=0 equation:

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

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

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

Multiply (2 + u) * (5 + u)
(2(5 + u) + u(5 + u)) = 0
((5 * 2 + u * 2) + u(5 + u)) = 0
((10 + 2u) + u(5 + u)) = 0
(10 + 2u + (5 * u + u * u)) = 0
(10 + 2u + (5u + u2)) = 0

Combine like terms: 2u + 5u = 7u
(10 + 7u + u2) = 0

Solving
10 + 7u + u2 = 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}