(2u-3)(6-u)=0

Solution for (2u-3)(6-u)=0 equation:

Simplifying
(2u + -3)(6 + -1u) = 0

Reorder the terms:
(-3 + 2u)(6 + -1u) = 0

Multiply (-3 + 2u) * (6 + -1u)
(-3(6 + -1u) + 2u * (6 + -1u)) = 0
((6 * -3 + -1u * -3) + 2u * (6 + -1u)) = 0
((-18 + 3u) + 2u * (6 + -1u)) = 0
(-18 + 3u + (6 * 2u + -1u * 2u)) = 0
(-18 + 3u + (12u + -2u2)) = 0

Combine like terms: 3u + 12u = 15u
(-18 + 15u + -2u2) = 0

Solving
-18 + 15u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + u)(3 + -2u) = 0

Subproblem 1
Set the factor '(-6 + u)' equal to zero and attempt to solve:

Simplifying
-6 + u = 0

Solving
-6 + u = 0

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

Add '6' to each side of the equation.
-6 + 6 + u = 0 + 6

Combine like terms: -6 + 6 = 0
0 + u = 0 + 6
u = 0 + 6

Combine like terms: 0 + 6 = 6
u = 6

Simplifying
u = 6
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 = {6, 1.5}