(k-6)(k+1)=0

Solution for (k-6)(k+1)=0 equation:

Simplifying
(k + -6)(k + 1) = 0

Reorder the terms:
(-6 + k)(k + 1) = 0

Reorder the terms:
(-6 + k)(1 + k) = 0

Multiply (-6 + k) * (1 + k)
(-6(1 + k) + k(1 + k)) = 0
((1 * -6 + k * -6) + k(1 + k)) = 0
((-6 + -6k) + k(1 + k)) = 0
(-6 + -6k + (1 * k + k * k)) = 0
(-6 + -6k + (1k + k2)) = 0

Combine like terms: -6k + 1k = -5k
(-6 + -5k + k2) = 0

Solving
-6 + -5k + k2 = 0

Solving for variable 'k'.

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

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

Simplifying
-1 + -1k = 0

Solving
-1 + -1k = 0

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

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

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

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

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

Simplifying
k = -1
Subproblem 2
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
Solution
k = {-1, 6}