(2u-7)(1-u)=0

Solution for (2u-7)(1-u)=0 equation:

Simplifying
(2u + -7)(1 + -1u) = 0

Reorder the terms:
(-7 + 2u)(1 + -1u) = 0

Multiply (-7 + 2u) * (1 + -1u)
(-7(1 + -1u) + 2u * (1 + -1u)) = 0
((1 * -7 + -1u * -7) + 2u * (1 + -1u)) = 0
((-7 + 7u) + 2u * (1 + -1u)) = 0
(-7 + 7u + (1 * 2u + -1u * 2u)) = 0
(-7 + 7u + (2u + -2u2)) = 0

Combine like terms: 7u + 2u = 9u
(-7 + 9u + -2u2) = 0

Solving
-7 + 9u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-7 + 2u)(1 + -1u) = 0

Subproblem 1
Set the factor '(-7 + 2u)' equal to zero and attempt to solve:

Simplifying
-7 + 2u = 0

Solving
-7 + 2u = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2u = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2u = 0 + 7
2u = 0 + 7

Combine like terms: 0 + 7 = 7
2u = 7

Divide each side by '2'.
u = 3.5

Simplifying
u = 3.5
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 = {3.5, 1}