(4u+2)(6+u)=0

Solution for (4u+2)(6+u)=0 equation:

Simplifying
(4u + 2)(6 + u) = 0

Reorder the terms:
(2 + 4u)(6 + u) = 0

Multiply (2 + 4u) * (6 + u)
(2(6 + u) + 4u * (6 + u)) = 0
((6 * 2 + u * 2) + 4u * (6 + u)) = 0
((12 + 2u) + 4u * (6 + u)) = 0
(12 + 2u + (6 * 4u + u * 4u)) = 0
(12 + 2u + (24u + 4u2)) = 0

Combine like terms: 2u + 24u = 26u
(12 + 26u + 4u2) = 0

Solving
12 + 26u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 13u + 2u2) = 0

Factor a trinomial.
2((6 + u)(1 + 2u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + u)' equal to zero and attempt to solve:

Simplifying
6 + u = 0

Solving
6 + u = 0

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

Add '-6' to each side of the equation.
6 + -6 + u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + u = 0 + -6
u = 0 + -6

Combine like terms: 0 + -6 = -6
u = -6

Simplifying
u = -6
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 = {-6, -0.5}