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

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

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

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

Multiply (2 + -1u) * (-3 + 2u)
(2(-3 + 2u) + -1u * (-3 + 2u)) = 0
((-3 * 2 + 2u * 2) + -1u * (-3 + 2u)) = 0
((-6 + 4u) + -1u * (-3 + 2u)) = 0
(-6 + 4u + (-3 * -1u + 2u * -1u)) = 0
(-6 + 4u + (3u + -2u2)) = 0

Combine like terms: 4u + 3u = 7u
(-6 + 7u + -2u2) = 0

Solving
-6 + 7u + -2u2 = 0

Solving for variable 'u'.

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

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

Simplifying
-2 + u = 0

Solving
-2 + u = 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 + u = 0 + 2

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

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

Simplifying
u = 2
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 = {2, 1.5}