4k^2+11k=-6

Solution for 4k^2+11k=-6 equation:

Simplifying
4k2 + 11k = -6

Reorder the terms:
11k + 4k2 = -6

Solving
11k + 4k2 = -6

Solving for variable 'k'.

Reorder the terms:
6 + 11k + 4k2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 11k + 4k2 = 0

Factor a trinomial.
(2 + k)(3 + 4k) = 0

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 '(3 + 4k)' equal to zero and attempt to solve:

Simplifying
3 + 4k = 0

Solving
3 + 4k = 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 + 4k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4k = 0 + -3
4k = 0 + -3

Combine like terms: 0 + -3 = -3
4k = -3

Divide each side by '4'.
k = -0.75

Simplifying
k = -0.75
Solution
k = {-2, -0.75}