7k^2=-11k-4

Solution for 7k^2=-11k-4 equation:

Simplifying
7k2 = -11k + -4

Reorder the terms:
7k2 = -4 + -11k

Solving
7k2 = -4 + -11k

Solving for variable 'k'.

Reorder the terms:
4 + 11k + 7k2 = -4 + -11k + 4 + 11k

Reorder the terms:
4 + 11k + 7k2 = -4 + 4 + -11k + 11k

Combine like terms: -4 + 4 = 0
4 + 11k + 7k2 = 0 + -11k + 11k
4 + 11k + 7k2 = -11k + 11k

Combine like terms: -11k + 11k = 0
4 + 11k + 7k2 = 0

Factor a trinomial.
(1 + k)(4 + 7k) = 0

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 '(4 + 7k)' equal to zero and attempt to solve:

Simplifying
4 + 7k = 0

Solving
4 + 7k = 0

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

Add '-4' to each side of the equation.
4 + -4 + 7k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7k = 0 + -4
7k = 0 + -4

Combine like terms: 0 + -4 = -4
7k = -4

Divide each side by '7'.
k = -0.5714285714

Simplifying
k = -0.5714285714
Solution
k = {-1, -0.5714285714}