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

Solution for (1-u)(2u-3)=0 equation:

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

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

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

Combine like terms: 2u + 3u = 5u
(-3 + 5u + -2u2) = 0

Solving
-3 + 5u + -2u2 = 0

Solving for variable 'u'.

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

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

Simplifying
1 + -1u = 0

Solving
1 + -1u = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1u = 0 + -1

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

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

Divide each side by '-1'.
u = 1

Simplifying
u = 1
Solution
u = {1.5, 1}