(4u+6)(3+u)=0

Solution for (4u+6)(3+u)=0 equation:

Simplifying
(4u + 6)(3 + u) = 0

Reorder the terms:
(6 + 4u)(3 + u) = 0

Multiply (6 + 4u) * (3 + u)
(6(3 + u) + 4u * (3 + u)) = 0
((3 * 6 + u * 6) + 4u * (3 + u)) = 0
((18 + 6u) + 4u * (3 + u)) = 0
(18 + 6u + (3 * 4u + u * 4u)) = 0
(18 + 6u + (12u + 4u2)) = 0

Combine like terms: 6u + 12u = 18u
(18 + 18u + 4u2) = 0

Solving
18 + 18u + 4u2 = 0

Solving for variable 'u'.

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

Factor a trinomial.
2((3 + u)(3 + 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 '(3 + 2u)' equal to zero and attempt to solve:

Simplifying
3 + 2u = 0

Solving
3 + 2u = 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 + 2u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2u = 0 + -3
2u = 0 + -3

Combine like terms: 0 + -3 = -3
2u = -3

Divide each side by '2'.
u = -1.5

Simplifying
u = -1.5
Solution
u = {-3, -1.5}