m^2(12m+4)-5m=0

Solution for m^2(12m+4)-5m=0 equation:

Simplifying
m2(12m + 4) + -5m = 0

Reorder the terms:
m2(4 + 12m) + -5m = 0
(4 * m2 + 12m * m2) + -5m = 0
(4m2 + 12m3) + -5m = 0

Reorder the terms:
-5m + 4m2 + 12m3 = 0

Solving
-5m + 4m2 + 12m3 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'm'.
m(-5 + 4m + 12m2) = 0

Factor a trinomial.
m((-5 + -6m)(1 + -2m)) = 0

Subproblem 1
Set the factor 'm' equal to zero and attempt to solve:

Simplifying
m = 0

Solving
m = 0

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

Simplifying
m = 0
Subproblem 2
Set the factor '(-5 + -6m)' equal to zero and attempt to solve:

Simplifying
-5 + -6m = 0

Solving
-5 + -6m = 0

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

Add '5' to each side of the equation.
-5 + 5 + -6m = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6m = 0 + 5
-6m = 0 + 5

Combine like terms: 0 + 5 = 5
-6m = 5

Divide each side by '-6'.
m = -0.8333333333

Simplifying
m = -0.8333333333
Subproblem 3
Set the factor '(1 + -2m)' equal to zero and attempt to solve:

Simplifying
1 + -2m = 0

Solving
1 + -2m = 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 + -2m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2m = 0 + -1
-2m = 0 + -1

Combine like terms: 0 + -1 = -1
-2m = -1

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

Simplifying
m = 0.5
Solution
m = {0, -0.8333333333, 0.5}