(4u+7)(6-u)=0

Solution for (4u+7)(6-u)=0 equation:

Simplifying
(4u + 7)(6 + -1u) = 0

Reorder the terms:
(7 + 4u)(6 + -1u) = 0

Multiply (7 + 4u) * (6 + -1u)
(7(6 + -1u) + 4u * (6 + -1u)) = 0
((6 * 7 + -1u * 7) + 4u * (6 + -1u)) = 0
((42 + -7u) + 4u * (6 + -1u)) = 0
(42 + -7u + (6 * 4u + -1u * 4u)) = 0
(42 + -7u + (24u + -4u2)) = 0

Combine like terms: -7u + 24u = 17u
(42 + 17u + -4u2) = 0

Solving
42 + 17u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + -1u)(7 + 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 '(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
Solution
u = {6, -1.75}