m^2+3m-4s^2=0

Solution for m^2+3m-4s^2=0 equation:

Simplifying
m2 + 3m + -4s2 = 0

Reorder the terms:
3m + m2 + -4s2 = 0

Solving
3m + m2 + -4s2 = 0

Solving for variable 'm'.

Factor a trinomial.
(m + -1s)(m + 4s) = 0

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

Simplifying
m + -1s = 0

Solving
m + -1s = 0

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

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

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

Simplifying
m = s
Subproblem 2
Set the factor '(m + 4s)' equal to zero and attempt to solve:

Simplifying
m + 4s = 0

Solving
m + 4s = 0

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

Add '-4s' to each side of the equation.
m + 4s + -4s = 0 + -4s

Combine like terms: 4s + -4s = 0
m + 0 = 0 + -4s
m = 0 + -4s
Remove the zero:
m = -4s

Simplifying
m = -4s
Solution
m = {s, -4s}