5k^2+23k=10

Solution for 5k^2+23k=10 equation:

Simplifying
5k2 + 23k = 10

Reorder the terms:
23k + 5k2 = 10

Solving
23k + 5k2 = 10

Solving for variable 'k'.

Reorder the terms:
-10 + 23k + 5k2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 23k + 5k2 = 0

Factor a trinomial.
(-5 + -1k)(2 + -5k) = 0

Subproblem 1
Set the factor '(-5 + -1k)' equal to zero and attempt to solve:

Simplifying
-5 + -1k = 0

Solving
-5 + -1k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1k = 0 + 5
-1k = 0 + 5

Combine like terms: 0 + 5 = 5
-1k = 5

Divide each side by '-1'.
k = -5

Simplifying
k = -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 = {-5, 0.4}