3m^3(2m^2-5m+3)-4m(m^4+2m^3-m^2)=

Solution for 3m^3(2m^2-5m+3)-4m(m^4+2m^3-m^2)= equation:

Simplifying
3m3(2m2 + -5m + 3) + -4m(m4 + 2m3 + -1m2) = 0

Reorder the terms:
3m3(3 + -5m + 2m2) + -4m(m4 + 2m3 + -1m2) = 0
(3 * 3m3 + -5m * 3m3 + 2m2 * 3m3) + -4m(m4 + 2m3 + -1m2) = 0
(9m3 + -15m4 + 6m5) + -4m(m4 + 2m3 + -1m2) = 0

Reorder the terms:
9m3 + -15m4 + 6m5 + -4m(-1m2 + 2m3 + m4) = 0
9m3 + -15m4 + 6m5 + (-1m2 * -4m + 2m3 * -4m + m4 * -4m) = 0
9m3 + -15m4 + 6m5 + (4m3 + -8m4 + -4m5) = 0

Reorder the terms:
9m3 + 4m3 + -15m4 + -8m4 + 6m5 + -4m5 = 0

Combine like terms: 9m3 + 4m3 = 13m3
13m3 + -15m4 + -8m4 + 6m5 + -4m5 = 0

Combine like terms: -15m4 + -8m4 = -23m4
13m3 + -23m4 + 6m5 + -4m5 = 0

Combine like terms: 6m5 + -4m5 = 2m5
13m3 + -23m4 + 2m5 = 0

Solving
13m3 + -23m4 + 2m5 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'm3'.
m3(13 + -23m + 2m2) = 0

Subproblem 1
Set the factor 'm3' equal to zero and attempt to solve:

Simplifying
m3 = 0

Solving
m3 = 0

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

Simplifying
m3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(13 + -23m + 2m2)' equal to zero and attempt to solve:

Simplifying
13 + -23m + 2m2 = 0

Solving
13 + -23m + 2m2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
6.5 + -11.5m + m2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -11.5m + -6.5 + m2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -11.5m + m2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -11.5m + m2 = 0 + -6.5
-11.5m + m2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-11.5m + m2 = -6.5

The m term is -11.5m.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5m + 33.0625 + m2 = -6.5 + 33.0625

Reorder the terms:
33.0625 + -11.5m + m2 = -6.5 + 33.0625

Combine like terms: -6.5 + 33.0625 = 26.5625
33.0625 + -11.5m + m2 = 26.5625

Factor a perfect square on the left side:
(m + -5.75)(m + -5.75) = 26.5625

Calculate the square root of the right side: 5.153882032

Break this problem into two subproblems by setting 
(m + -5.75) equal to 5.153882032 and -5.153882032.

Subproblem 1
m + -5.75 = 5.153882032

Simplifying
m + -5.75 = 5.153882032

Reorder the terms:
-5.75 + m = 5.153882032

Solving
-5.75 + m = 5.153882032

Solving for variable 'm'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + m = 5.153882032 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + m = 5.153882032 + 5.75
m = 5.153882032 + 5.75

Combine like terms: 5.153882032 + 5.75 = 10.903882032
m = 10.903882032

Simplifying
m = 10.903882032

Subproblem 2
m + -5.75 = -5.153882032

Simplifying
m + -5.75 = -5.153882032

Reorder the terms:
-5.75 + m = -5.153882032

Solving
-5.75 + m = -5.153882032

Solving for variable 'm'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + m = -5.153882032 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + m = -5.153882032 + 5.75
m = -5.153882032 + 5.75

Combine like terms: -5.153882032 + 5.75 = 0.596117968
m = 0.596117968

Simplifying
m = 0.596117968

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {10.903882032, 0.596117968}
Solution
m = {10.903882032, 0.596117968}