=2m^3-4m^2+20m

Solution for =2m^3-4m^2+20m equation:

Simplifying
0 = 2m3 + -4m2 + 20m

Reorder the terms:
0 = 20m + -4m2 + 2m3

Solving
0 = 20m + -4m2 + 2m3

Solving for variable 'm'.
Remove the zero:
-20m + 4m2 + -2m3 = 20m + -4m2 + 2m3 + -20m + 4m2 + -2m3

Reorder the terms:
-20m + 4m2 + -2m3 = 20m + -20m + -4m2 + 4m2 + 2m3 + -2m3

Combine like terms: 20m + -20m = 0
-20m + 4m2 + -2m3 = 0 + -4m2 + 4m2 + 2m3 + -2m3
-20m + 4m2 + -2m3 = -4m2 + 4m2 + 2m3 + -2m3

Combine like terms: -4m2 + 4m2 = 0
-20m + 4m2 + -2m3 = 0 + 2m3 + -2m3
-20m + 4m2 + -2m3 = 2m3 + -2m3

Combine like terms: 2m3 + -2m3 = 0
-20m + 4m2 + -2m3 = 0

Factor out the Greatest Common Factor (GCF), '2m'.
2m(-10 + 2m + -1m2) = 0

Ignore the factor 2.
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 '(-10 + 2m + -1m2)' equal to zero and attempt to solve:

Simplifying
-10 + 2m + -1m2 = 0

Solving
-10 + 2m + -1m2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
10 + -2m + m2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -2m + -10 + m2 = 0 + -10

Reorder the terms:
10 + -10 + -2m + m2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -2m + m2 = 0 + -10
-2m + m2 = 0 + -10

Combine like terms: 0 + -10 = -10
-2m + m2 = -10

The m term is -2m.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m + 1 + m2 = -10 + 1

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

Combine like terms: -10 + 1 = -9
1 + -2m + m2 = -9

Factor a perfect square on the left side:
(m + -1)(m + -1) = -9

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
m = {0}