(2u-5)(6+u)=0

Solution for (2u-5)(6+u)=0 equation:

Simplifying
(2u + -5)(6 + u) = 0

Reorder the terms:
(-5 + 2u)(6 + u) = 0

Multiply (-5 + 2u) * (6 + u)
(-5(6 + u) + 2u * (6 + u)) = 0
((6 * -5 + u * -5) + 2u * (6 + u)) = 0
((-30 + -5u) + 2u * (6 + u)) = 0
(-30 + -5u + (6 * 2u + u * 2u)) = 0
(-30 + -5u + (12u + 2u2)) = 0

Combine like terms: -5u + 12u = 7u
(-30 + 7u + 2u2) = 0

Solving
-30 + 7u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + -1u)(5 + -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 '(5 + -2u)' equal to zero and attempt to solve:

Simplifying
5 + -2u = 0

Solving
5 + -2u = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2u = 0 + -5
-2u = 0 + -5

Combine like terms: 0 + -5 = -5
-2u = -5

Divide each side by '-2'.
u = 2.5

Simplifying
u = 2.5
Solution
u = {-6, 2.5}