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

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

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

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

Multiply (4 + u) * (2 + 4u)
(4(2 + 4u) + u(2 + 4u)) = 0
((2 * 4 + 4u * 4) + u(2 + 4u)) = 0
((8 + 16u) + u(2 + 4u)) = 0
(8 + 16u + (2 * u + 4u * u)) = 0
(8 + 16u + (2u + 4u2)) = 0

Combine like terms: 16u + 2u = 18u
(8 + 18u + 4u2) = 0

Solving
8 + 18u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 9u + 2u2) = 0

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

Ignore the factor 2.
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}