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

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

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

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

Multiply (1 + 4u) * (6 + -1u)
(1(6 + -1u) + 4u * (6 + -1u)) = 0
((6 * 1 + -1u * 1) + 4u * (6 + -1u)) = 0
((6 + -1u) + 4u * (6 + -1u)) = 0
(6 + -1u + (6 * 4u + -1u * 4u)) = 0
(6 + -1u + (24u + -4u2)) = 0

Combine like terms: -1u + 24u = 23u
(6 + 23u + -4u2) = 0

Solving
6 + 23u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + -1u)(1 + 4u) = 0

Subproblem 1
Set the factor '(6 + -1u)' equal to zero and attempt to solve:

Simplifying
6 + -1u = 0

Solving
6 + -1u = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
u = 6

Simplifying
u = 6
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 = {6, -0.25}