3k(k+2)=-3

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

Simplifying
3k(k + 2) = -3

Reorder the terms:
3k(2 + k) = -3
(2 * 3k + k * 3k) = -3
(6k + 3k2) = -3

Solving
6k + 3k2 = -3

Solving for variable 'k'.

Reorder the terms:
3 + 6k + 3k2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 6k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 2k + k2) = 0

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

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

Simplifying
1 + k = 0

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

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

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

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

Simplifying
1 + k = 0

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

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

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

Simplifying
k = -1
Solution
k = {-1, -1}