(1*m^2)*x^2+8mx+12=0

Solution for (1*m^2)*x^2+8mx+12=0 equation:

Simplifying
(1m2) * x2 + 8mx + 12 = 0

Remove parenthesis around (1m2)
1m2 * x2 + 8mx + 12 = 0

Multiply m2 * x2
1m2x2 + 8mx + 12 = 0

Reorder the terms:
12 + 8mx + 1m2x2 = 0

Solving
12 + 8mx + 1m2x2 = 0

Solving for variable 'm'.

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

Subproblem 1
Set the factor '(6 + mx)' equal to zero and attempt to solve:

Simplifying
6 + mx = 0

Solving
6 + mx = 0

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

Add '-6' to each side of the equation.
6 + -6 + mx = 0 + -6

Combine like terms: 6 + -6 = 0
0 + mx = 0 + -6
mx = 0 + -6

Combine like terms: 0 + -6 = -6
mx = -6

Divide each side by 'x'.
m = -6x-1

Simplifying
m = -6x-1
Subproblem 2
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
Solution
m = {-6x-1, -2x-1}