m^2(3m-7)=6m

Solution for m^2(3m-7)=6m equation:

Simplifying
m2(3m + -7) = 6m

Reorder the terms:
m2(-7 + 3m) = 6m
(-7 * m2 + 3m * m2) = 6m
(-7m2 + 3m3) = 6m

Solving
-7m2 + 3m3 = 6m

Solving for variable 'm'.

Reorder the terms:
-6m + -7m2 + 3m3 = 6m + -6m

Combine like terms: 6m + -6m = 0
-6m + -7m2 + 3m3 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(-6 + -7m + 3m2) = 0

Factor a trinomial.
m((-2 + -3m)(3 + -1m)) = 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 '(-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
Subproblem 3
Set the factor '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

Solving
3 + -1m = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1m = 0 + -3
-1m = 0 + -3

Combine like terms: 0 + -3 = -3
-1m = -3

Divide each side by '-1'.
m = 3

Simplifying
m = 3
Solution
m = {0, -0.6666666667, 3}