(3k-1)(k-5)=0

Solution for (3k-1)(k-5)=0 equation:

Simplifying
(3k + -1)(k + -5) = 0

Reorder the terms:
(-1 + 3k)(k + -5) = 0

Reorder the terms:
(-1 + 3k)(-5 + k) = 0

Multiply (-1 + 3k) * (-5 + k)
(-1(-5 + k) + 3k * (-5 + k)) = 0
((-5 * -1 + k * -1) + 3k * (-5 + k)) = 0
((5 + -1k) + 3k * (-5 + k)) = 0
(5 + -1k + (-5 * 3k + k * 3k)) = 0
(5 + -1k + (-15k + 3k2)) = 0

Combine like terms: -1k + -15k = -16k
(5 + -16k + 3k2) = 0

Solving
5 + -16k + 3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(1 + -3k)(5 + -1k) = 0

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

Simplifying
1 + -3k = 0

Solving
1 + -3k = 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 + -3k = 0 + -1

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

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

Divide each side by '-3'.
k = 0.3333333333

Simplifying
k = 0.3333333333
Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {0.3333333333, 5}