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

Solution for 4*(k+2)*(k+2)=0 equation:

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

Reorder the terms:
4(2 + k)(k + 2) = 0

Reorder the terms:
4(2 + k)(2 + k) = 0

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

Combine like terms: 2k + 2k = 4k
4(4 + 4k + k2) = 0
(4 * 4 + 4k * 4 + k2 * 4) = 0
(16 + 16k + 4k2) = 0

Solving
16 + 16k + 4k2 = 0

Solving for variable 'k'.

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

Factor a trinomial.
4((2 + k)(2 + k)) = 0

Ignore the factor 4.
Subproblem 1
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 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
Solution
k = {-2, -2}