(4u+2)(3+u)=0

Solution for (4u+2)(3+u)=0 equation:

Simplifying
(4u + 2)(3 + u) = 0

Reorder the terms:
(2 + 4u)(3 + u) = 0

Multiply (2 + 4u) * (3 + u)
(2(3 + u) + 4u * (3 + u)) = 0
((3 * 2 + u * 2) + 4u * (3 + u)) = 0
((6 + 2u) + 4u * (3 + u)) = 0
(6 + 2u + (3 * 4u + u * 4u)) = 0
(6 + 2u + (12u + 4u2)) = 0

Combine like terms: 2u + 12u = 14u
(6 + 14u + 4u2) = 0

Solving
6 + 14u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 7u + 2u2) = 0

Factor a trinomial.
2((3 + u)(1 + 2u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

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

Add '-3' to each side of the equation.
3 + -3 + u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + u = 0 + -3
u = 0 + -3

Combine like terms: 0 + -3 = -3
u = -3

Simplifying
u = -3
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 = {-3, -0.5}