7k^2=-9k-2

Solution for 7k^2=-9k-2 equation:

Simplifying
7k2 = -9k + -2

Reorder the terms:
7k2 = -2 + -9k

Solving
7k2 = -2 + -9k

Solving for variable 'k'.

Reorder the terms:
2 + 9k + 7k2 = -2 + -9k + 2 + 9k

Reorder the terms:
2 + 9k + 7k2 = -2 + 2 + -9k + 9k

Combine like terms: -2 + 2 = 0
2 + 9k + 7k2 = 0 + -9k + 9k
2 + 9k + 7k2 = -9k + 9k

Combine like terms: -9k + 9k = 0
2 + 9k + 7k2 = 0

Factor a trinomial.
(1 + k)(2 + 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 '(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}