(3u-2)(3+u)=0

Solution for (3u-2)(3+u)=0 equation:

Simplifying
(3u + -2)(3 + u) = 0

Reorder the terms:
(-2 + 3u)(3 + u) = 0

Multiply (-2 + 3u) * (3 + u)
(-2(3 + u) + 3u * (3 + u)) = 0
((3 * -2 + u * -2) + 3u * (3 + u)) = 0
((-6 + -2u) + 3u * (3 + u)) = 0
(-6 + -2u + (3 * 3u + u * 3u)) = 0
(-6 + -2u + (9u + 3u2)) = 0

Combine like terms: -2u + 9u = 7u
(-6 + 7u + 3u2) = 0

Solving
-6 + 7u + 3u2 = 0

Solving for variable 'u'.

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

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 '(2 + -3u)' equal to zero and attempt to solve:

Simplifying
2 + -3u = 0

Solving
2 + -3u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3u = 0 + -2

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

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

Divide each side by '-3'.
u = 0.6666666667

Simplifying
u = 0.6666666667
Solution
u = {-3, 0.6666666667}