m^2(5m+1)=6m

Solution for m^2(5m+1)=6m equation:

Simplifying
m2(5m + 1) = 6m

Reorder the terms:
m2(1 + 5m) = 6m
(1 * m2 + 5m * m2) = 6m
(1m2 + 5m3) = 6m

Solving
1m2 + 5m3 = 6m

Solving for variable 'm'.

Reorder the terms:
-6m + 1m2 + 5m3 = 6m + -6m

Combine like terms: 6m + -6m = 0
-6m + 1m2 + 5m3 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(-6 + m + 5m2) = 0

Factor a trinomial.
m((-6 + -5m)(1 + -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 '(-6 + -5m)' equal to zero and attempt to solve:

Simplifying
-6 + -5m = 0

Solving
-6 + -5m = 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 + -5m = 0 + 6

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

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

Divide each side by '-5'.
m = -1.2

Simplifying
m = -1.2
Subproblem 3
Set the factor '(1 + -1m)' equal to zero and attempt to solve:

Simplifying
1 + -1m = 0

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

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

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

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

Simplifying
m = 1
Solution
m = {0, -1.2, 1}