5m^2n(m^2-3m+1)=

Solution for 5m^2n(m^2-3m+1)= equation:

Simplifying
5m2n(m2 + -3m + 1) = 0

Reorder the terms:
5m2n(1 + -3m + m2) = 0
(1 * 5m2n + -3m * 5m2n + m2 * 5m2n) = 0
(5m2n + -15m3n + 5m4n) = 0

Solving
5m2n + -15m3n + 5m4n = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '5m2n'.
5m2n(1 + -3m + m2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'm2n' equal to zero and attempt to solve:

Simplifying
m2n = 0

Solving
m2n = 0

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

Simplifying
m2n = 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 '(1 + -3m + m2)' equal to zero and attempt to solve:

Simplifying
1 + -3m + m2 = 0

Solving
1 + -3m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3m + -1 + m2 = 0 + -1

Reorder the terms:
1 + -1 + -3m + m2 = 0 + -1

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

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

The m term is -3m.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3m + 2.25 + m2 = -1 + 2.25

Reorder the terms:
2.25 + -3m + m2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3m + m2 = 1.25

Factor a perfect square on the left side:
(m + -1.5)(m + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(m + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
m + -1.5 = 1.118033989

Simplifying
m + -1.5 = 1.118033989

Reorder the terms:
-1.5 + m = 1.118033989

Solving
-1.5 + m = 1.118033989

Solving for variable 'm'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + m = 1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + m = 1.118033989 + 1.5
m = 1.118033989 + 1.5

Combine like terms: 1.118033989 + 1.5 = 2.618033989
m = 2.618033989

Simplifying
m = 2.618033989

Subproblem 2
m + -1.5 = -1.118033989

Simplifying
m + -1.5 = -1.118033989

Reorder the terms:
-1.5 + m = -1.118033989

Solving
-1.5 + m = -1.118033989

Solving for variable 'm'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + m = -1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + m = -1.118033989 + 1.5
m = -1.118033989 + 1.5

Combine like terms: -1.118033989 + 1.5 = 0.381966011
m = 0.381966011

Simplifying
m = 0.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.618033989, 0.381966011}
Solution
m = {2.618033989, 0.381966011}