k^2+5kn-84n^2=0

Solution for k^2+5kn-84n^2=0 equation:

Simplifying
k2 + 5kn + -84n2 = 0

Reorder the terms:
5kn + k2 + -84n2 = 0

Solving
5kn + k2 + -84n2 = 0

Solving for variable 'k'.

Factor a trinomial.
(k + -7n)(k + 12n) = 0

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

Simplifying
k + -7n = 0

Solving
k + -7n = 0

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

Add '7n' to each side of the equation.
k + -7n + 7n = 0 + 7n

Combine like terms: -7n + 7n = 0
k + 0 = 0 + 7n
k = 0 + 7n
Remove the zero:
k = 7n

Simplifying
k = 7n
Subproblem 2
Set the factor '(k + 12n)' equal to zero and attempt to solve:

Simplifying
k + 12n = 0

Solving
k + 12n = 0

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

Add '-12n' to each side of the equation.
k + 12n + -12n = 0 + -12n

Combine like terms: 12n + -12n = 0
k + 0 = 0 + -12n
k = 0 + -12n
Remove the zero:
k = -12n

Simplifying
k = -12n
Solution
k = {7n, -12n}