(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 = 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}