(4u+6)(1+u)=0

Solution for (4u+6)(1+u)=0 equation:

Simplifying
(4u + 6)(1 + u) = 0

Reorder the terms:
(6 + 4u)(1 + u) = 0

Multiply (6 + 4u) * (1 + u)
(6(1 + u) + 4u * (1 + u)) = 0
((1 * 6 + u * 6) + 4u * (1 + u)) = 0
((6 + 6u) + 4u * (1 + u)) = 0
(6 + 6u + (1 * 4u + u * 4u)) = 0
(6 + 6u + (4u + 4u2)) = 0

Combine like terms: 6u + 4u = 10u
(6 + 10u + 4u2) = 0

Solving
6 + 10u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 5u + 2u2) = 0

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

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

Simplifying
1 + u = 0

Solving
1 + u = 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 + u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + u = 0 + -1
u = 0 + -1

Combine like terms: 0 + -1 = -1
u = -1

Simplifying
u = -1
Solution
u = {-1.5, -1}