(4k+6)(k+1)=0

Solution for (4k+6)(k+1)=0 equation:

Simplifying
(4k + 6)(k + 1) = 0

Reorder the terms:
(6 + 4k)(k + 1) = 0

Reorder the terms:
(6 + 4k)(1 + k) = 0

Multiply (6 + 4k) * (1 + k)
(6(1 + k) + 4k * (1 + k)) = 0
((1 * 6 + k * 6) + 4k * (1 + k)) = 0
((6 + 6k) + 4k * (1 + k)) = 0
(6 + 6k + (1 * 4k + k * 4k)) = 0
(6 + 6k + (4k + 4k2)) = 0

Combine like terms: 6k + 4k = 10k
(6 + 10k + 4k2) = 0

Solving
6 + 10k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 5k + 2k2) = 0

Factor a trinomial.
2((3 + 2k)(1 + k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 2k)' equal to zero and attempt to solve:

Simplifying
3 + 2k = 0

Solving
3 + 2k = 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 + 2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2k = 0 + -3
2k = 0 + -3

Combine like terms: 0 + -3 = -3
2k = -3

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
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 = {-1.5, -1}