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

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

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

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

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

Multiply (3 + 2k) * (1 + 5k)
(3(1 + 5k) + 2k * (1 + 5k)) = 0
((1 * 3 + 5k * 3) + 2k * (1 + 5k)) = 0
((3 + 15k) + 2k * (1 + 5k)) = 0
(3 + 15k + (1 * 2k + 5k * 2k)) = 0
(3 + 15k + (2k + 10k2)) = 0

Combine like terms: 15k + 2k = 17k
(3 + 17k + 10k2) = 0

Solving
3 + 17k + 10k2 = 0

Solving for variable 'k'.

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

Subproblem 1
Set the factor '(3 + 2k)' equal to zero and attempt to solve:

Simplifying
3 + 2k = 0

Solving
3 + 2k = 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 + 2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2k = 0 + -3
2k = 0 + -3

Combine like terms: 0 + -3 = -3
2k = -3

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
Subproblem 2
Set the factor '(1 + 5k)' equal to zero and attempt to solve:

Simplifying
1 + 5k = 0

Solving
1 + 5k = 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 + 5k = 0 + -1

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

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

Divide each side by '5'.
k = -0.2

Simplifying
k = -0.2
Solution
k = {-1.5, -0.2}