(k-7)(k-6)=0

Solution for (k-7)(k-6)=0 equation:

Simplifying
(k + -7)(k + -6) = 0

Reorder the terms:
(-7 + k)(k + -6) = 0

Reorder the terms:
(-7 + k)(-6 + k) = 0

Multiply (-7 + k) * (-6 + k)
(-7(-6 + k) + k(-6 + k)) = 0
((-6 * -7 + k * -7) + k(-6 + k)) = 0
((42 + -7k) + k(-6 + k)) = 0
(42 + -7k + (-6 * k + k * k)) = 0
(42 + -7k + (-6k + k2)) = 0

Combine like terms: -7k + -6k = -13k
(42 + -13k + k2) = 0

Solving
42 + -13k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(6 + -1k)(7 + -1k) = 0

Subproblem 1
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 0

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

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

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

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

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

Simplifying
k = 6
Subproblem 2
Set the factor '(7 + -1k)' equal to zero and attempt to solve:

Simplifying
7 + -1k = 0

Solving
7 + -1k = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1k = 0 + -7
-1k = 0 + -7

Combine like terms: 0 + -7 = -7
-1k = -7

Divide each side by '-1'.
k = 7

Simplifying
k = 7
Solution
k = {6, 7}