7k^2+5k-8=-6

Solution for 7k^2+5k-8=-6 equation:

Simplifying
7k2 + 5k + -8 = -6

Reorder the terms:
-8 + 5k + 7k2 = -6

Solving
-8 + 5k + 7k2 = -6

Solving for variable 'k'.

Reorder the terms:
-8 + 6 + 5k + 7k2 = -6 + 6

Combine like terms: -8 + 6 = -2
-2 + 5k + 7k2 = -6 + 6

Combine like terms: -6 + 6 = 0
-2 + 5k + 7k2 = 0

Factor a trinomial.
(-1 + -1k)(2 + -7k) = 0

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

Simplifying
-1 + -1k = 0

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

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

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

Divide each side by '-1'.
k = -1

Simplifying
k = -1
Subproblem 2
Set the factor '(2 + -7k)' equal to zero and attempt to solve:

Simplifying
2 + -7k = 0

Solving
2 + -7k = 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 + -7k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7k = 0 + -2
-7k = 0 + -2

Combine like terms: 0 + -2 = -2
-7k = -2

Divide each side by '-7'.
k = 0.2857142857

Simplifying
k = 0.2857142857
Solution
k = {-1, 0.2857142857}