(4u-6)(1-u)=0

Solution for (4u-6)(1-u)=0 equation:

Simplifying
(4u + -6)(1 + -1u) = 0

Reorder the terms:
(-6 + 4u)(1 + -1u) = 0

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

Combine like terms: 6u + 4u = 10u
(-6 + 10u + -4u2) = 0

Solving
-6 + 10u + -4u2 = 0

Solving for variable 'u'.

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

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

Ignore the factor 2.
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}