x^2-3kx-18k^2=0

Solution for x^2-3kx-18k^2=0 equation:

Simplifying
x2 + -3kx + -18k2 = 0

Reorder the terms:
-3kx + -18k2 + x2 = 0

Solving
-3kx + -18k2 + x2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-3k + -1x)(6k + -1x) = 0

Subproblem 1
Set the factor '(-3k + -1x)' equal to zero and attempt to solve:

Simplifying
-3k + -1x = 0

Solving
-3k + -1x = 0

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

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

Combine like terms: -1x + x = 0
-3k + 0 = 0 + x
-3k = 0 + x
Remove the zero:
-3k = x

Divide each side by '-3'.
k = -0.3333333333x

Simplifying
k = -0.3333333333x
Subproblem 2
Set the factor '(6k + -1x)' equal to zero and attempt to solve:

Simplifying
6k + -1x = 0

Solving
6k + -1x = 0

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

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

Combine like terms: -1x + x = 0
6k + 0 = 0 + x
6k = 0 + x
Remove the zero:
6k = x

Divide each side by '6'.
k = 0.1666666667x

Simplifying
k = 0.1666666667x
Solution
k = {-0.3333333333x, 0.1666666667x}