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((-3 + -1m)(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 '(-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
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, -3, 0.6666666667}