m^2(8m+6)=5m

Solution for m^2(8m+6)=5m equation:

Simplifying
m2(8m + 6) = 5m

Reorder the terms:
m2(6 + 8m) = 5m
(6 * m2 + 8m * m2) = 5m
(6m2 + 8m3) = 5m

Solving
6m2 + 8m3 = 5m

Solving for variable 'm'.

Reorder the terms:
-5m + 6m2 + 8m3 = 5m + -5m

Combine like terms: 5m + -5m = 0
-5m + 6m2 + 8m3 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(-5 + 6m + 8m2) = 0

Factor a trinomial.
m((-5 + -4m)(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 + -4m)' equal to zero and attempt to solve:

Simplifying
-5 + -4m = 0

Solving
-5 + -4m = 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 + -4m = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4m = 0 + 5
-4m = 0 + 5

Combine like terms: 0 + 5 = 5
-4m = 5

Divide each side by '-4'.
m = -1.25

Simplifying
m = -1.25
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, -1.25, 0.5}