(k-6)(k-1)=-k-2

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Solution for (k-6)(k-1)=-k-2 equation: 


Simplifying
(k + -6)(k + -1) = -1k + -2

Reorder the terms:
(-6 + k)(k + -1) = -1k + -2

Reorder the terms:
(-6 + k)(-1 + k) = -1k + -2

Multiply (-6 + k) * (-1 + k)
(-6(-1 + k) + k(-1 + k)) = -1k + -2
((-1 * -6 + k * -6) + k(-1 + k)) = -1k + -2
((6 + -6k) + k(-1 + k)) = -1k + -2
(6 + -6k + (-1 * k + k * k)) = -1k + -2
(6 + -6k + (-1k + k2)) = -1k + -2

Combine like terms: -6k + -1k = -7k
(6 + -7k + k2) = -1k + -2

Reorder the terms:
6 + -7k + k2 = -2 + -1k

Solving
6 + -7k + k2 = -2 + -1k

Solving for variable 'k'.

Reorder the terms:
6 + 2 + -7k + k + k2 = -2 + -1k + 2 + k

Combine like terms: 6 + 2 = 8
8 + -7k + k + k2 = -2 + -1k + 2 + k

Combine like terms: -7k + k = -6k
8 + -6k + k2 = -2 + -1k + 2 + k

Reorder the terms:
8 + -6k + k2 = -2 + 2 + -1k + k

Combine like terms: -2 + 2 = 0
8 + -6k + k2 = 0 + -1k + k
8 + -6k + k2 = -1k + k

Combine like terms: -1k + k = 0
8 + -6k + k2 = 0

Factor a trinomial.
(2 + -1k)(4 + -1k) = 0


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

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2

Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {2, 4}

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