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

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

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

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

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

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

Solving
2 + 9u + 4u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

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

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

Simplifying
u = -2
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 = {-2, -0.25}