(2u-3)(3u-4)=0

Solution for (2u-3)(3u-4)=0 equation:

Simplifying
(2u + -3)(3u + -4) = 0

Reorder the terms:
(-3 + 2u)(3u + -4) = 0

Reorder the terms:
(-3 + 2u)(-4 + 3u) = 0

Multiply (-3 + 2u) * (-4 + 3u)
(-3(-4 + 3u) + 2u * (-4 + 3u)) = 0
((-4 * -3 + 3u * -3) + 2u * (-4 + 3u)) = 0
((12 + -9u) + 2u * (-4 + 3u)) = 0
(12 + -9u + (-4 * 2u + 3u * 2u)) = 0
(12 + -9u + (-8u + 6u2)) = 0

Combine like terms: -9u + -8u = -17u
(12 + -17u + 6u2) = 0

Solving
12 + -17u + 6u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4 + -3u)(3 + -2u) = 0

Subproblem 1
Set the factor '(4 + -3u)' equal to zero and attempt to solve:

Simplifying
4 + -3u = 0

Solving
4 + -3u = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3u = 0 + -4
-3u = 0 + -4

Combine like terms: 0 + -4 = -4
-3u = -4

Divide each side by '-3'.
u = 1.333333333

Simplifying
u = 1.333333333
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 = {1.333333333, 1.5}