10k^2+31k-9=5

Solution for 10k^2+31k-9=5 equation:

Simplifying
10k2 + 31k + -9 = 5

Reorder the terms:
-9 + 31k + 10k2 = 5

Solving
-9 + 31k + 10k2 = 5

Solving for variable 'k'.

Reorder the terms:
-9 + -5 + 31k + 10k2 = 5 + -5

Combine like terms: -9 + -5 = -14
-14 + 31k + 10k2 = 5 + -5

Combine like terms: 5 + -5 = 0
-14 + 31k + 10k2 = 0

Factor a trinomial.
(-7 + -2k)(2 + -5k) = 0

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

Simplifying
-7 + -2k = 0

Solving
-7 + -2k = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2k = 0 + 7

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

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

Divide each side by '-2'.
k = -3.5

Simplifying
k = -3.5
Subproblem 2
Set the factor '(2 + -5k)' equal to zero and attempt to solve:

Simplifying
2 + -5k = 0

Solving
2 + -5k = 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 + -5k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5k = 0 + -2
-5k = 0 + -2

Combine like terms: 0 + -2 = -2
-5k = -2

Divide each side by '-5'.
k = 0.4

Simplifying
k = 0.4
Solution
k = {-3.5, 0.4}