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

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

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

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

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

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

Combine like terms: 6k + 5k = 11k
k(15 + 11k + 2k2) = 0
(15 * k + 11k * k + 2k2 * k) = 0
(15k + 11k2 + 2k3) = 0

Solving
15k + 11k2 + 2k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(15 + 11k + 2k2) = 0

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

Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

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

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

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

Simplifying
k = -3
Subproblem 3
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
Solution
k = {0, -3, -2.5}