4k^2+7k-102=0

Solution for 4k^2+7k-102=0 equation:

Simplifying
4k2 + 7k + -102 = 0

Reorder the terms:
-102 + 7k + 4k2 = 0

Solving
-102 + 7k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-6 + -1k)(17 + -4k) = 0

Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(17 + -4k)' equal to zero and attempt to solve:

Simplifying
17 + -4k = 0

Solving
17 + -4k = 0

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

Add '-17' to each side of the equation.
17 + -17 + -4k = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -4k = 0 + -17
-4k = 0 + -17

Combine like terms: 0 + -17 = -17
-4k = -17

Divide each side by '-4'.
k = 4.25

Simplifying
k = 4.25
Solution
k = {-6, 4.25}