(1-u)(4u-7)=0

Solution for (1-u)(4u-7)=0 equation:

Simplifying
(1 + -1u)(4u + -7) = 0

Reorder the terms:
(1 + -1u)(-7 + 4u) = 0

Multiply (1 + -1u) * (-7 + 4u)
(1(-7 + 4u) + -1u * (-7 + 4u)) = 0
((-7 * 1 + 4u * 1) + -1u * (-7 + 4u)) = 0
((-7 + 4u) + -1u * (-7 + 4u)) = 0
(-7 + 4u + (-7 * -1u + 4u * -1u)) = 0
(-7 + 4u + (7u + -4u2)) = 0

Combine like terms: 4u + 7u = 11u
(-7 + 11u + -4u2) = 0

Solving
-7 + 11u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-7 + 4u)(1 + -1u) = 0

Subproblem 1
Set the factor '(-7 + 4u)' equal to zero and attempt to solve:

Simplifying
-7 + 4u = 0

Solving
-7 + 4u = 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 + 4u = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4u = 0 + 7
4u = 0 + 7

Combine like terms: 0 + 7 = 7
4u = 7

Divide each side by '4'.
u = 1.75

Simplifying
u = 1.75
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 = {1.75, 1}