(2u-2)(6u-9)=0

Solution for (2u-2)(6u-9)=0 equation:

Simplifying
(2u + -2)(6u + -9) = 0

Reorder the terms:
(-2 + 2u)(6u + -9) = 0

Reorder the terms:
(-2 + 2u)(-9 + 6u) = 0

Multiply (-2 + 2u) * (-9 + 6u)
(-2(-9 + 6u) + 2u * (-9 + 6u)) = 0
((-9 * -2 + 6u * -2) + 2u * (-9 + 6u)) = 0
((18 + -12u) + 2u * (-9 + 6u)) = 0
(18 + -12u + (-9 * 2u + 6u * 2u)) = 0
(18 + -12u + (-18u + 12u2)) = 0

Combine like terms: -12u + -18u = -30u
(18 + -30u + 12u2) = 0

Solving
18 + -30u + 12u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -5u + 2u2) = 0

Factor a trinomial.
6((1 + -1u)(3 + -2u)) = 0

Ignore the factor 6.
Subproblem 1
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
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, 1.5}