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

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

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

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

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

Combine like terms: 12u + 2u = 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}