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

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

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

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

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

Multiply (-1 + 3k) * (3 + 5k)
(-1(3 + 5k) + 3k * (3 + 5k)) = 0
((3 * -1 + 5k * -1) + 3k * (3 + 5k)) = 0
((-3 + -5k) + 3k * (3 + 5k)) = 0
(-3 + -5k + (3 * 3k + 5k * 3k)) = 0
(-3 + -5k + (9k + 15k2)) = 0

Combine like terms: -5k + 9k = 4k
(-3 + 4k + 15k2) = 0

Solving
-3 + 4k + 15k2 = 0

Solving for variable 'k'.

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

Subproblem 1
Set the factor '(-3 + -5k)' equal to zero and attempt to solve:

Simplifying
-3 + -5k = 0

Solving
-3 + -5k = 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 + -5k = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5k = 0 + 3
-5k = 0 + 3

Combine like terms: 0 + 3 = 3
-5k = 3

Divide each side by '-5'.
k = -0.6

Simplifying
k = -0.6
Subproblem 2
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
Solution
k = {-0.6, 0.3333333333}