-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 = -4u
-2(5 + -4u + -1u2) = 0
(5 * -2 + -4u * -2 + -1u2 * -2) = 0
(-10 + 8u + 2u2) = 0

Solving
-10 + 8u + 2u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 4u + u2) = 0

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

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

Simplifying
-5 + -1u = 0

Solving
-5 + -1u = 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 + -1u = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1u = 0 + 5
-1u = 0 + 5

Combine like terms: 0 + 5 = 5
-1u = 5

Divide each side by '-1'.
u = -5

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

Simplifying
1 + -1u = 0

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

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

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

Divide each side by '-1'.
u = 1

Simplifying
u = 1
Solution
u = {-5, 1}