3(m-3)(m-2)=3m

Solution for 3(m-3)(m-2)=3m equation:

Simplifying
3(m + -3)(m + -2) = 3m

Reorder the terms:
3(-3 + m)(m + -2) = 3m

Reorder the terms:
3(-3 + m)(-2 + m) = 3m

Multiply (-3 + m) * (-2 + m)
3(-3(-2 + m) + m(-2 + m)) = 3m
3((-2 * -3 + m * -3) + m(-2 + m)) = 3m
3((6 + -3m) + m(-2 + m)) = 3m
3(6 + -3m + (-2 * m + m * m)) = 3m
3(6 + -3m + (-2m + m2)) = 3m

Combine like terms: -3m + -2m = -5m
3(6 + -5m + m2) = 3m
(6 * 3 + -5m * 3 + m2 * 3) = 3m
(18 + -15m + 3m2) = 3m

Solving
18 + -15m + 3m2 = 3m

Solving for variable 'm'.

Reorder the terms:
18 + -15m + -3m + 3m2 = 3m + -3m

Combine like terms: -15m + -3m = -18m
18 + -18m + 3m2 = 3m + -3m

Combine like terms: 3m + -3m = 0
18 + -18m + 3m2 = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -6m + m2)' equal to zero and attempt to solve:

Simplifying
6 + -6m + m2 = 0

Solving
6 + -6m + m2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -6 + 9

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

Combine like terms: -6 + 9 = 3
9 + -6m + m2 = 3

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

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(m + -3) equal to 1.732050808 and -1.732050808.

Subproblem 1
m + -3 = 1.732050808

Simplifying
m + -3 = 1.732050808

Reorder the terms:
-3 + m = 1.732050808

Solving
-3 + m = 1.732050808

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = 1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + m = 1.732050808 + 3
m = 1.732050808 + 3

Combine like terms: 1.732050808 + 3 = 4.732050808
m = 4.732050808

Simplifying
m = 4.732050808

Subproblem 2
m + -3 = -1.732050808

Simplifying
m + -3 = -1.732050808

Reorder the terms:
-3 + m = -1.732050808

Solving
-3 + m = -1.732050808

Solving for variable 'm'.

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

Add '3' to each side of the equation.
-3 + 3 + m = -1.732050808 + 3

Combine like terms: -3 + 3 = 0
0 + m = -1.732050808 + 3
m = -1.732050808 + 3

Combine like terms: -1.732050808 + 3 = 1.267949192
m = 1.267949192

Simplifying
m = 1.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.732050808, 1.267949192}
Solution
m = {4.732050808, 1.267949192}