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

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

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

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

Multiply (1 + 4u) * (4 + u)
(1(4 + u) + 4u * (4 + u)) = 0
((4 * 1 + u * 1) + 4u * (4 + u)) = 0
((4 + 1u) + 4u * (4 + u)) = 0
(4 + 1u + (4 * 4u + u * 4u)) = 0
(4 + 1u + (16u + 4u2)) = 0

Combine like terms: 1u + 16u = 17u
(4 + 17u + 4u2) = 0

Solving
4 + 17u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4 + u)(1 + 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 '(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 = {-4, -0.25}