(k-6)(7k-2)=0

Solution for (k-6)(7k-2)=0 equation:

Simplifying
(k + -6)(7k + -2) = 0

Reorder the terms:
(-6 + k)(7k + -2) = 0

Reorder the terms:
(-6 + k)(-2 + 7k) = 0

Multiply (-6 + k) * (-2 + 7k)
(-6(-2 + 7k) + k(-2 + 7k)) = 0
((-2 * -6 + 7k * -6) + k(-2 + 7k)) = 0
((12 + -42k) + k(-2 + 7k)) = 0
(12 + -42k + (-2 * k + 7k * k)) = 0
(12 + -42k + (-2k + 7k2)) = 0

Combine like terms: -42k + -2k = -44k
(12 + -44k + 7k2) = 0

Solving
12 + -44k + 7k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(2 + -7k)(6 + -1k) = 0

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

Simplifying
2 + -7k = 0

Solving
2 + -7k = 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 + -7k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7k = 0 + -2
-7k = 0 + -2

Combine like terms: 0 + -2 = -2
-7k = -2

Divide each side by '-7'.
k = 0.2857142857

Simplifying
k = 0.2857142857
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 = {0.2857142857, 6}