k(k+2)k(k+2)=0

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Solution for k(k+2)k(k+2)=0 equation: 


Simplifying
k(k + 2) * k(k + 2) = 0

Reorder the terms:
k(2 + k) * k(k + 2) = 0

Reorder the terms:
k(2 + k) * k(2 + k) = 0

Reorder the terms for easier multiplication:
k * k(2 + k)(2 + k) = 0

Multiply k * k
k2(2 + k)(2 + k) = 0

Multiply (2 + k) * (2 + k)
k2(2(2 + k) + k(2 + k)) = 0
k2((2 * 2 + k * 2) + k(2 + k)) = 0
k2((4 + 2k) + k(2 + k)) = 0
k2(4 + 2k + (2 * k + k * k)) = 0
k2(4 + 2k + (2k + k2)) = 0

Combine like terms: 2k + 2k = 4k
k2(4 + 4k + k2) = 0
(4 * k2 + 4k * k2 + k2 * k2) = 0
(4k2 + 4k3 + k4) = 0

Solving
4k2 + 4k3 + k4 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k2'.
k2(4 + 4k + k2) = 0

Factor a trinomial.
k2((2 + k)(2 + k)) = 0


Subproblem 1
Set the factor 'k2' equal to zero and attempt to solve:

Simplifying
k2 = 0

Solving
k2 = 0

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

Simplifying
k2 = 0

Take the square root of each side:
k = {0}

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

Simplifying
2 + k = 0

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

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

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

Simplifying
k = -2

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

Simplifying
2 + k = 0

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

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

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

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

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