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

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

Simplifying
(4u + 6)(3 + -1u) = 0

Reorder the terms:
(6 + 4u)(3 + -1u) = 0

Multiply (6 + 4u) * (3 + -1u)
(6(3 + -1u) + 4u * (3 + -1u)) = 0
((3 * 6 + -1u * 6) + 4u * (3 + -1u)) = 0
((18 + -6u) + 4u * (3 + -1u)) = 0
(18 + -6u + (3 * 4u + -1u * 4u)) = 0
(18 + -6u + (12u + -4u2)) = 0

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

Solving
18 + 6u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 3u + -2u2) = 0

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

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

Simplifying
3 + -1u = 0

Solving
3 + -1u = 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 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
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}