12k^2=-7k-1

Solution for 12k^2=-7k-1 equation:

Simplifying
12k2 = -7k + -1

Reorder the terms:
12k2 = -1 + -7k

Solving
12k2 = -1 + -7k

Solving for variable 'k'.

Reorder the terms:
1 + 7k + 12k2 = -1 + -7k + 1 + 7k

Reorder the terms:
1 + 7k + 12k2 = -1 + 1 + -7k + 7k

Combine like terms: -1 + 1 = 0
1 + 7k + 12k2 = 0 + -7k + 7k
1 + 7k + 12k2 = -7k + 7k

Combine like terms: -7k + 7k = 0
1 + 7k + 12k2 = 0

Factor a trinomial.
(1 + 3k)(1 + 4k) = 0

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

Simplifying
1 + 3k = 0

Solving
1 + 3k = 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 + 3k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3k = 0 + -1
3k = 0 + -1

Combine like terms: 0 + -1 = -1
3k = -1

Divide each side by '3'.
k = -0.3333333333

Simplifying
k = -0.3333333333
Subproblem 2
Set the factor '(1 + 4k)' equal to zero and attempt to solve:

Simplifying
1 + 4k = 0

Solving
1 + 4k = 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 + 4k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4k = 0 + -1
4k = 0 + -1

Combine like terms: 0 + -1 = -1
4k = -1

Divide each side by '4'.
k = -0.25

Simplifying
k = -0.25
Solution
k = {-0.3333333333, -0.25}