x^2+mx-6m^2=0

Solution for x^2+mx-6m^2=0 equation:

Simplifying
x2 + mx + -6m2 = 0

Reorder the terms:
mx + -6m2 + x2 = 0

Solving
mx + -6m2 + x2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-3m + -1x)(2m + -1x) = 0

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

Simplifying
-3m + -1x = 0

Solving
-3m + -1x = 0

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

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

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

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

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

Simplifying
2m + -1x = 0

Solving
2m + -1x = 0

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

Add 'x' to each side of the equation.
2m + -1x + x = 0 + x

Combine like terms: -1x + x = 0
2m + 0 = 0 + x
2m = 0 + x
Remove the zero:
2m = x

Divide each side by '2'.
m = 0.5x

Simplifying
m = 0.5x
Solution
m = {-0.3333333333x, 0.5x}