(2u+7)(6-u)=0

Solution for (2u+7)(6-u)=0 equation:

Simplifying
(2u + 7)(6 + -1u) = 0

Reorder the terms:
(7 + 2u)(6 + -1u) = 0

Multiply (7 + 2u) * (6 + -1u)
(7(6 + -1u) + 2u * (6 + -1u)) = 0
((6 * 7 + -1u * 7) + 2u * (6 + -1u)) = 0
((42 + -7u) + 2u * (6 + -1u)) = 0
(42 + -7u + (6 * 2u + -1u * 2u)) = 0
(42 + -7u + (12u + -2u2)) = 0

Combine like terms: -7u + 12u = 5u
(42 + 5u + -2u2) = 0

Solving
42 + 5u + -2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + -1u)(7 + 2u) = 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 + 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
Solution
u = {6, -3.5}