m^2x^2+3mx+2=0

Solution for m^2x^2+3mx+2=0 equation:

Simplifying
m2x2 + 3mx + 2 = 0

Reorder the terms:
2 + 3mx + m2x2 = 0

Solving
2 + 3mx + m2x2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2 + mx)(1 + mx) = 0

Subproblem 1
Set the factor '(2 + mx)' equal to zero and attempt to solve:

Simplifying
2 + mx = 0

Solving
2 + mx = 0

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

Add '-2' to each side of the equation.
2 + -2 + mx = 0 + -2

Combine like terms: 2 + -2 = 0
0 + mx = 0 + -2
mx = 0 + -2

Combine like terms: 0 + -2 = -2
mx = -2

Divide each side by 'x'.
m = -2x-1

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

Simplifying
1 + mx = 0

Solving
1 + mx = 0

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

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

Combine like terms: 1 + -1 = 0
0 + mx = 0 + -1
mx = 0 + -1

Combine like terms: 0 + -1 = -1
mx = -1

Divide each side by 'x'.
m = -1x-1

Simplifying
m = -1x-1
Solution
m = {-2x-1, -1x-1}