(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.
(-1 + -3k)(3 + -5k) = 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 '(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
Solution
k = {-0.3333333333, 0.6}