4(u+5)(u+1)=0

Solution for 4(u+5)(u+1)=0 equation:

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

Reorder the terms:
4(5 + u)(u + 1) = 0

Reorder the terms:
4(5 + u)(1 + u) = 0

Multiply (5 + u) * (1 + u)
4(5(1 + u) + u(1 + u)) = 0
4((1 * 5 + u * 5) + u(1 + u)) = 0
4((5 + 5u) + u(1 + u)) = 0
4(5 + 5u + (1 * u + u * u)) = 0
4(5 + 5u + (1u + u2)) = 0

Combine like terms: 5u + 1u = 6u
4(5 + 6u + u2) = 0
(5 * 4 + 6u * 4 + u2 * 4) = 0
(20 + 24u + 4u2) = 0

Solving
20 + 24u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 6u + u2) = 0

Factor a trinomial.
4((5 + u)(1 + u)) = 0

Ignore the factor 4.
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}