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

Solution for (9-u)(4u-1)=0 equation:

Simplifying
(9 + -1u)(4u + -1) = 0

Reorder the terms:
(9 + -1u)(-1 + 4u) = 0

Multiply (9 + -1u) * (-1 + 4u)
(9(-1 + 4u) + -1u * (-1 + 4u)) = 0
((-1 * 9 + 4u * 9) + -1u * (-1 + 4u)) = 0
((-9 + 36u) + -1u * (-1 + 4u)) = 0
(-9 + 36u + (-1 * -1u + 4u * -1u)) = 0
(-9 + 36u + (1u + -4u2)) = 0

Combine like terms: 36u + 1u = 37u
(-9 + 37u + -4u2) = 0

Solving
-9 + 37u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-9 + u)(1 + -4u) = 0

Subproblem 1
Set the factor '(-9 + u)' equal to zero and attempt to solve:

Simplifying
-9 + u = 0

Solving
-9 + u = 0

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

Add '9' to each side of the equation.
-9 + 9 + u = 0 + 9

Combine like terms: -9 + 9 = 0
0 + u = 0 + 9
u = 0 + 9

Combine like terms: 0 + 9 = 9
u = 9

Simplifying
u = 9
Subproblem 2
Set the factor '(1 + -4u)' equal to zero and attempt to solve:

Simplifying
1 + -4u = 0

Solving
1 + -4u = 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 + -4u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4u = 0 + -1
-4u = 0 + -1

Combine like terms: 0 + -1 = -1
-4u = -1

Divide each side by '-4'.
u = 0.25

Simplifying
u = 0.25
Solution
u = {9, 0.25}