10k^2+k-9=0

Solution for 10k^2+k-9=0 equation:

Simplifying
10k2 + k + -9 = 0

Reorder the terms:
-9 + k + 10k2 = 0

Solving
-9 + k + 10k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-1 + -1k)(9 + -10k) = 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 '(9 + -10k)' equal to zero and attempt to solve:

Simplifying
9 + -10k = 0

Solving
9 + -10k = 0

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

Add '-9' to each side of the equation.
9 + -9 + -10k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -10k = 0 + -9
-10k = 0 + -9

Combine like terms: 0 + -9 = -9
-10k = -9

Divide each side by '-10'.
k = 0.9

Simplifying
k = 0.9
Solution
k = {-1, 0.9}