10m^3+6m^2-2m=3m^2-m

Solution for 10m^3+6m^2-2m=3m^2-m equation:

Simplifying
10m3 + 6m2 + -2m = 3m2 + -1m

Reorder the terms:
-2m + 6m2 + 10m3 = 3m2 + -1m

Reorder the terms:
-2m + 6m2 + 10m3 = -1m + 3m2

Solving
-2m + 6m2 + 10m3 = -1m + 3m2

Solving for variable 'm'.

Reorder the terms:
-2m + m + 6m2 + -3m2 + 10m3 = -1m + 3m2 + m + -3m2

Combine like terms: -2m + m = -1m
-1m + 6m2 + -3m2 + 10m3 = -1m + 3m2 + m + -3m2

Combine like terms: 6m2 + -3m2 = 3m2
-1m + 3m2 + 10m3 = -1m + 3m2 + m + -3m2

Reorder the terms:
-1m + 3m2 + 10m3 = -1m + m + 3m2 + -3m2

Combine like terms: -1m + m = 0
-1m + 3m2 + 10m3 = 0 + 3m2 + -3m2
-1m + 3m2 + 10m3 = 3m2 + -3m2

Combine like terms: 3m2 + -3m2 = 0
-1m + 3m2 + 10m3 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(-1 + 3m + 10m2) = 0

Factor a trinomial.
m((-1 + -2m)(1 + -5m)) = 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 '(-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
Subproblem 3
Set the factor '(1 + -5m)' equal to zero and attempt to solve:

Simplifying
1 + -5m = 0

Solving
1 + -5m = 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 + -5m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5m = 0 + -1
-5m = 0 + -1

Combine like terms: 0 + -1 = -1
-5m = -1

Divide each side by '-5'.
m = 0.2

Simplifying
m = 0.2
Solution
m = {0, -0.5, 0.2}