(k-6)(k-1)=-k-3

Solution for (k-6)(k-1)=-k-3 equation:

Simplifying
(k + -6)(k + -1) = -1k + -3

Reorder the terms:
(-6 + k)(k + -1) = -1k + -3

Reorder the terms:
(-6 + k)(-1 + k) = -1k + -3

Multiply (-6 + k) * (-1 + k)
(-6(-1 + k) + k(-1 + k)) = -1k + -3
((-1 * -6 + k * -6) + k(-1 + k)) = -1k + -3
((6 + -6k) + k(-1 + k)) = -1k + -3
(6 + -6k + (-1 * k + k * k)) = -1k + -3
(6 + -6k + (-1k + k2)) = -1k + -3

Combine like terms: -6k + -1k = -7k
(6 + -7k + k2) = -1k + -3

Reorder the terms:
6 + -7k + k2 = -3 + -1k

Solving
6 + -7k + k2 = -3 + -1k

Solving for variable 'k'.

Reorder the terms:
6 + 3 + -7k + k + k2 = -3 + -1k + 3 + k

Combine like terms: 6 + 3 = 9
9 + -7k + k + k2 = -3 + -1k + 3 + k

Combine like terms: -7k + k = -6k
9 + -6k + k2 = -3 + -1k + 3 + k

Reorder the terms:
9 + -6k + k2 = -3 + 3 + -1k + k

Combine like terms: -3 + 3 = 0
9 + -6k + k2 = 0 + -1k + k
9 + -6k + k2 = -1k + k

Combine like terms: -1k + k = 0
9 + -6k + k2 = 0

Factor a trinomial.
(3 + -1k)(3 + -1k) = 0

Subproblem 1
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {3, 3}