10(2k^2-k-15)=0

Solution for 10(2k^2-k-15)=0 equation:

Simplifying
10(2k2 + -1k + -15) = 0

Reorder the terms:
10(-15 + -1k + 2k2) = 0
(-15 * 10 + -1k * 10 + 2k2 * 10) = 0
(-150 + -10k + 20k2) = 0

Solving
-150 + -10k + 20k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-15 + -1k + 2k2) = 0

Factor a trinomial.
10((-5 + -2k)(3 + -1k)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-5 + -2k)' equal to zero and attempt to solve:

Simplifying
-5 + -2k = 0

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

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

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

Divide each side by '-2'.
k = -2.5

Simplifying
k = -2.5
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {-2.5, 3}