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

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

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

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

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

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

Combine like terms: -6u + -5u = -11u
(30 + -11u + u2) = 0

Solving
30 + -11u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(5 + -1u)(6 + -1u) = 0

Subproblem 1
Set the factor '(5 + -1u)' equal to zero and attempt to solve:

Simplifying
5 + -1u = 0

Solving
5 + -1u = 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 + -1u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1u = 0 + -5
-1u = 0 + -5

Combine like terms: 0 + -5 = -5
-1u = -5

Divide each side by '-1'.
u = 5

Simplifying
u = 5
Subproblem 2
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
Solution
u = {5, 6}