m^2(9m+6)=8m

Solution for m^2(9m+6)=8m equation:

Simplifying
m2(9m + 6) = 8m

Reorder the terms:
m2(6 + 9m) = 8m
(6 * m2 + 9m * m2) = 8m
(6m2 + 9m3) = 8m

Solving
6m2 + 9m3 = 8m

Solving for variable 'm'.

Reorder the terms:
-8m + 6m2 + 9m3 = 8m + -8m

Combine like terms: 8m + -8m = 0
-8m + 6m2 + 9m3 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(-8 + 6m + 9m2) = 0

Factor a trinomial.
m((-4 + -3m)(2 + -3m)) = 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 '(-4 + -3m)' equal to zero and attempt to solve:

Simplifying
-4 + -3m = 0

Solving
-4 + -3m = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3m = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3m = 0 + 4
-3m = 0 + 4

Combine like terms: 0 + 4 = 4
-3m = 4

Divide each side by '-3'.
m = -1.333333333

Simplifying
m = -1.333333333
Subproblem 3
Set the factor '(2 + -3m)' equal to zero and attempt to solve:

Simplifying
2 + -3m = 0

Solving
2 + -3m = 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 + -3m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3m = 0 + -2
-3m = 0 + -2

Combine like terms: 0 + -2 = -2
-3m = -2

Divide each side by '-3'.
m = 0.6666666667

Simplifying
m = 0.6666666667
Solution
m = {0, -1.333333333, 0.6666666667}