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

Solution for -2(u+5)(-u-1)=0 equation:

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

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

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

Multiply (5 + u) * (-1 + -1u)
-2(5(-1 + -1u) + u(-1 + -1u)) = 0
-2((-1 * 5 + -1u * 5) + u(-1 + -1u)) = 0
-2((-5 + -5u) + u(-1 + -1u)) = 0
-2(-5 + -5u + (-1 * u + -1u * u)) = 0
-2(-5 + -5u + (-1u + -1u2)) = 0

Combine like terms: -5u + -1u = -6u
-2(-5 + -6u + -1u2) = 0
(-5 * -2 + -6u * -2 + -1u2 * -2) = 0
(10 + 12u + 2u2) = 0

Solving
10 + 12u + 2u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 6u + u2) = 0

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

Ignore the factor 2.
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 + 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 = {-5, -1}