(v-5)(v-6)=0

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

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

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

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

Multiply (-5 + v) * (-6 + v)
(-5(-6 + v) + v(-6 + v)) = 0
((-6 * -5 + v * -5) + v(-6 + v)) = 0
((30 + -5v) + v(-6 + v)) = 0
(30 + -5v + (-6 * v + v * v)) = 0
(30 + -5v + (-6v + v2)) = 0

Combine like terms: -5v + -6v = -11v
(30 + -11v + v2) = 0

Solving
30 + -11v + v2 = 0

Solving for variable 'v'.

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

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

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

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

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

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

Simplifying
v = 5
Subproblem 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

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

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

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

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

Simplifying
v = 6
Solution
v = {5, 6}