3m^3-18m^2+75m=0

Solution for 3m^3-18m^2+75m=0 equation:

Simplifying
3m3 + -18m2 + 75m = 0

Reorder the terms:
75m + -18m2 + 3m3 = 0

Solving
75m + -18m2 + 3m3 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3m'.
3m(25 + -6m + m2) = 0

Ignore the factor 3.
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 '(25 + -6m + m2)' equal to zero and attempt to solve:

Simplifying
25 + -6m + m2 = 0

Solving
25 + -6m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -6m + -25 + m2 = 0 + -25

Reorder the terms:
25 + -25 + -6m + m2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -6m + m2 = 0 + -25
-6m + m2 = 0 + -25

Combine like terms: 0 + -25 = -25
-6m + m2 = -25

The m term is -6m.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6m + 9 + m2 = -25 + 9

Reorder the terms:
9 + -6m + m2 = -25 + 9

Combine like terms: -25 + 9 = -16
9 + -6m + m2 = -16

Factor a perfect square on the left side:
(m + -3)(m + -3) = -16

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}