(4+u)(2u+1)=0

Solution for (4+u)(2u+1)=0 equation:

Simplifying
(4 + u)(2u + 1) = 0

Reorder the terms:
(4 + u)(1 + 2u) = 0

Multiply (4 + u) * (1 + 2u)
(4(1 + 2u) + u(1 + 2u)) = 0
((1 * 4 + 2u * 4) + u(1 + 2u)) = 0
((4 + 8u) + u(1 + 2u)) = 0
(4 + 8u + (1 * u + 2u * u)) = 0
(4 + 8u + (1u + 2u2)) = 0

Combine like terms: 8u + 1u = 9u
(4 + 9u + 2u2) = 0

Solving
4 + 9u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4 + u)(1 + 2u) = 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 + 2u)' equal to zero and attempt to solve:

Simplifying
1 + 2u = 0

Solving
1 + 2u = 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 + 2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2u = 0 + -1
2u = 0 + -1

Combine like terms: 0 + -1 = -1
2u = -1

Divide each side by '2'.
u = -0.5

Simplifying
u = -0.5
Solution
u = {-4, -0.5}