(2k+5)(3k-1)=0

Solution for (2k+5)(3k-1)=0 equation:

Simplifying
(2k + 5)(3k + -1) = 0

Reorder the terms:
(5 + 2k)(3k + -1) = 0

Reorder the terms:
(5 + 2k)(-1 + 3k) = 0

Multiply (5 + 2k) * (-1 + 3k)
(5(-1 + 3k) + 2k * (-1 + 3k)) = 0
((-1 * 5 + 3k * 5) + 2k * (-1 + 3k)) = 0
((-5 + 15k) + 2k * (-1 + 3k)) = 0
(-5 + 15k + (-1 * 2k + 3k * 2k)) = 0
(-5 + 15k + (-2k + 6k2)) = 0

Combine like terms: 15k + -2k = 13k
(-5 + 13k + 6k2) = 0

Solving
-5 + 13k + 6k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-5 + -2k)(1 + -3k) = 0

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

Simplifying
-5 + -2k = 0

Solving
-5 + -2k = 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 + -2k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2k = 0 + 5
-2k = 0 + 5

Combine like terms: 0 + 5 = 5
-2k = 5

Divide each side by '-2'.
k = -2.5

Simplifying
k = -2.5
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 = {-2.5, 0.3333333333}