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

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


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

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

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

Multiply (2 + k) * (-5 + 3k)
k(2(-5 + 3k) + k(-5 + 3k)) = 0
k((-5 * 2 + 3k * 2) + k(-5 + 3k)) = 0
k((-10 + 6k) + k(-5 + 3k)) = 0
k(-10 + 6k + (-5 * k + 3k * k)) = 0
k(-10 + 6k + (-5k + 3k2)) = 0

Combine like terms: 6k + -5k = 1k
k(-10 + 1k + 3k2) = 0
(-10 * k + 1k * k + 3k2 * k) = 0
(-10k + 1k2 + 3k3) = 0

Solving
-10k + 1k2 + 3k3 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k'.
k(-10 + k + 3k2) = 0

Factor a trinomial.
k((-2 + -1k)(5 + -3k)) = 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 '(-2 + -1k)' equal to zero and attempt to solve:

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1k = 0 + 2
-1k = 0 + 2

Combine like terms: 0 + 2 = 2
-1k = 2

Divide each side by '-1'.
k = -2

Simplifying
k = -2

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

Simplifying
5 + -3k = 0

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

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

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

Divide each side by '-3'.
k = 1.666666667

Simplifying
k = 1.666666667
Solution
k = {0, -2, 1.666666667}

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