7k^2+43k-42=0

Solution for 7k^2+43k-42=0 equation:

Simplifying
7k2 + 43k + -42 = 0

Reorder the terms:
-42 + 43k + 7k2 = 0

Solving
-42 + 43k + 7k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-7 + -1k)(6 + -7k) = 0

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

Simplifying
-7 + -1k = 0

Solving
-7 + -1k = 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 + -1k = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1k = 0 + 7
-1k = 0 + 7

Combine like terms: 0 + 7 = 7
-1k = 7

Divide each side by '-1'.
k = -7

Simplifying
k = -7
Subproblem 2
Set the factor '(6 + -7k)' equal to zero and attempt to solve:

Simplifying
6 + -7k = 0

Solving
6 + -7k = 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 + -7k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7k = 0 + -6
-7k = 0 + -6

Combine like terms: 0 + -6 = -6
-7k = -6

Divide each side by '-7'.
k = 0.8571428571

Simplifying
k = 0.8571428571
Solution
k = {-7, 0.8571428571}