(7k-2)(2k-1)=0

Solution for (7k-2)(2k-1)=0 equation:

Simplifying
(7k + -2)(2k + -1) = 0

Reorder the terms:
(-2 + 7k)(2k + -1) = 0

Reorder the terms:
(-2 + 7k)(-1 + 2k) = 0

Multiply (-2 + 7k) * (-1 + 2k)
(-2(-1 + 2k) + 7k * (-1 + 2k)) = 0
((-1 * -2 + 2k * -2) + 7k * (-1 + 2k)) = 0
((2 + -4k) + 7k * (-1 + 2k)) = 0
(2 + -4k + (-1 * 7k + 2k * 7k)) = 0
(2 + -4k + (-7k + 14k2)) = 0

Combine like terms: -4k + -7k = -11k
(2 + -11k + 14k2) = 0

Solving
2 + -11k + 14k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(2 + -7k)(1 + -2k) = 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 '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 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 + -2k = 0 + -1

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

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

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {0.2857142857, 0.5}