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

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

Simplifying
(3 + -1u)(3u + -2) = 0

Reorder the terms:
(3 + -1u)(-2 + 3u) = 0

Multiply (3 + -1u) * (-2 + 3u)
(3(-2 + 3u) + -1u * (-2 + 3u)) = 0
((-2 * 3 + 3u * 3) + -1u * (-2 + 3u)) = 0
((-6 + 9u) + -1u * (-2 + 3u)) = 0
(-6 + 9u + (-2 * -1u + 3u * -1u)) = 0
(-6 + 9u + (2u + -3u2)) = 0

Combine like terms: 9u + 2u = 11u
(-6 + 11u + -3u2) = 0

Solving
-6 + 11u + -3u2 = 0

Solving for variable 'u'.

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

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 '(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}