(k-3m)(k+m)=0

Solution for (k-3m)(k+m)=0 equation:

Simplifying
(k + -3m)(k + m) = 0

Multiply (k + -3m) * (k + m)
(k(k + m) + -3m * (k + m)) = 0
((k * k + m * k) + -3m * (k + m)) = 0

Reorder the terms:
((km + k2) + -3m * (k + m)) = 0
((km + k2) + -3m * (k + m)) = 0
(km + k2 + (k * -3m + m * -3m)) = 0
(km + k2 + (-3km + -3m2)) = 0

Reorder the terms:
(km + -3km + k2 + -3m2) = 0

Combine like terms: km + -3km = -2km
(-2km + k2 + -3m2) = 0

Solving
-2km + k2 + -3m2 = 0

Solving for variable 'k'.

Factor a trinomial.
(k + -3m)(k + m) = 0

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

Simplifying
k + -3m = 0

Solving
k + -3m = 0

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

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

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

Simplifying
k = 3m
Subproblem 2
Set the factor '(k + m)' equal to zero and attempt to solve:

Simplifying
k + m = 0

Solving
k + m = 0

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

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

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

Simplifying
k = -1m
Solution
k = {3m, -1m}