-2k^2+7k+14=10

Solution for -2k^2+7k+14=10 equation:

Simplifying
-2k2 + 7k + 14 = 10

Reorder the terms:
14 + 7k + -2k2 = 10

Solving
14 + 7k + -2k2 = 10

Solving for variable 'k'.

Reorder the terms:
14 + -10 + 7k + -2k2 = 10 + -10

Combine like terms: 14 + -10 = 4
4 + 7k + -2k2 = 10 + -10

Combine like terms: 10 + -10 = 0
4 + 7k + -2k2 = 0

Factor a trinomial.
(4 + -1k)(1 + 2k) = 0

Subproblem 1
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Subproblem 2
Set the factor '(1 + 2k)' equal to zero and attempt to solve:

Simplifying
1 + 2k = 0

Solving
1 + 2k = 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 + 2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2k = 0 + -1
2k = 0 + -1

Combine like terms: 0 + -1 = -1
2k = -1

Divide each side by '2'.
k = -0.5

Simplifying
k = -0.5
Solution
k = {4, -0.5}