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

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

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

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

Multiply (1 + 4u) * (5 + u)
(1(5 + u) + 4u * (5 + u)) = 0
((5 * 1 + u * 1) + 4u * (5 + u)) = 0
((5 + 1u) + 4u * (5 + u)) = 0
(5 + 1u + (5 * 4u + u * 4u)) = 0
(5 + 1u + (20u + 4u2)) = 0

Combine like terms: 1u + 20u = 21u
(5 + 21u + 4u2) = 0

Solving
5 + 21u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(5 + u)(1 + 4u) = 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 '(1 + 4u)' equal to zero and attempt to solve:

Simplifying
1 + 4u = 0

Solving
1 + 4u = 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 + 4u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4u = 0 + -1
4u = 0 + -1

Combine like terms: 0 + -1 = -1
4u = -1

Divide each side by '4'.
u = -0.25

Simplifying
u = -0.25
Solution
u = {-5, -0.25}