2m(7m^3+5m^2-m)=

Solution for 2m(7m^3+5m^2-m)= equation:

Simplifying
2m(7m3 + 5m2 + -1m) = 0

Reorder the terms:
2m(-1m + 5m2 + 7m3) = 0
(-1m * 2m + 5m2 * 2m + 7m3 * 2m) = 0
(-2m2 + 10m3 + 14m4) = 0

Solving
-2m2 + 10m3 + 14m4 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2m2'.
2m2(-1 + 5m + 7m2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'm2' equal to zero and attempt to solve:

Simplifying
m2 = 0

Solving
m2 = 0

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

Simplifying
m2 = 0

Take the square root of each side:
m = {0}
Subproblem 2
Set the factor '(-1 + 5m + 7m2)' equal to zero and attempt to solve:

Simplifying
-1 + 5m + 7m2 = 0

Solving
-1 + 5m + 7m2 = 0

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

Divide each side by '7'.
-0.1428571429 + 0.7142857143m + m2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.7142857143m + 0.1428571429 + m2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 0.7142857143m + m2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 0.7142857143m + m2 = 0 + 0.1428571429
0.7142857143m + m2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
0.7142857143m + m2 = 0.1428571429

The m term is 0.7142857143m.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143m + 0.1275510204 + m2 = 0.1428571429 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143m + m2 = 0.1428571429 + 0.1275510204

Combine like terms: 0.1428571429 + 0.1275510204 = 0.2704081633
0.1275510204 + 0.7142857143m + m2 = 0.2704081633

Factor a perfect square on the left side:
(m + 0.3571428572)(m + 0.3571428572) = 0.2704081633

Calculate the square root of the right side: 0.520007849

Break this problem into two subproblems by setting 
(m + 0.3571428572) equal to 0.520007849 and -0.520007849.

Subproblem 1
m + 0.3571428572 = 0.520007849

Simplifying
m + 0.3571428572 = 0.520007849

Reorder the terms:
0.3571428572 + m = 0.520007849

Solving
0.3571428572 + m = 0.520007849

Solving for variable 'm'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + m = 0.520007849 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + m = 0.520007849 + -0.3571428572
m = 0.520007849 + -0.3571428572

Combine like terms: 0.520007849 + -0.3571428572 = 0.1628649918
m = 0.1628649918

Simplifying
m = 0.1628649918

Subproblem 2
m + 0.3571428572 = -0.520007849

Simplifying
m + 0.3571428572 = -0.520007849

Reorder the terms:
0.3571428572 + m = -0.520007849

Solving
0.3571428572 + m = -0.520007849

Solving for variable 'm'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + m = -0.520007849 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + m = -0.520007849 + -0.3571428572
m = -0.520007849 + -0.3571428572

Combine like terms: -0.520007849 + -0.3571428572 = -0.8771507062
m = -0.8771507062

Simplifying
m = -0.8771507062

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.1628649918, -0.8771507062}
Solution
m = {0, 0.1628649918, -0.8771507062}