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

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

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

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

Multiply (5 + 4u) * (4 + u)
(5(4 + u) + 4u * (4 + u)) = 0
((4 * 5 + u * 5) + 4u * (4 + u)) = 0
((20 + 5u) + 4u * (4 + u)) = 0
(20 + 5u + (4 * 4u + u * 4u)) = 0
(20 + 5u + (16u + 4u2)) = 0

Combine like terms: 5u + 16u = 21u
(20 + 21u + 4u2) = 0

Solving
20 + 21u + 4u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(4 + u)' equal to zero and attempt to solve:

Simplifying
4 + u = 0

Solving
4 + u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + u = 0 + -4

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

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

Simplifying
u = -4
Subproblem 2
Set the factor '(5 + 4u)' equal to zero and attempt to solve:

Simplifying
5 + 4u = 0

Solving
5 + 4u = 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 + 4u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4u = 0 + -5
4u = 0 + -5

Combine like terms: 0 + -5 = -5
4u = -5

Divide each side by '4'.
u = -1.25

Simplifying
u = -1.25
Solution
u = {-4, -1.25}